How to fix broken GPT, GUID and unmountable, no type volumes? I have a Macbook Pro with retina, Yosemite and 500GB hard drive.
I tried to install Windows using Bootcamp and accidentally deleted a partition, now my Mac cannot boot anymore.
This is the output from sudo gpt -r show disk0

  gpt show: disk0: Suspicious MBR at sector 0
    start       size  index  contents
        0          1         MBR
        1          1         Pri GPT header
        2         32         Pri GPT table
       34          6         
       40     409600      1  GPT part - C12A7328-F81F-11D2-BA4B-00A0C93EC93B
   409640  776617328      2  GPT part - FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFFFFFF
777026968    1269760      3  GPT part - 48465300-0000-11AA-AA11-00306543ECAC
778296728        616         
778297344  198807552      4  GPT part - 48465300-0000-11AA-AA11-00306543ECAC
977104896        131         
977105027         32         Sec GPT table
977105059          1         Sec GPT header


I only need to make the second partition at index 2 and type FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFFFFFF to be bootable again. This partition has FileVault 2 enabled.

But right now, I have no clue on what to do.

P/S: I Followed the instruction from @klanomath
Boot from a external hard drive with full Yosemite system
but at the last command to change the partition type

sudo gpt add -b 409640 -s 776617328 -i 2 -t 53746F72-6167-11AA-AA11-00306543ECAC /dev/disk0


It got this error:

gpt add: /dev/disk0: Suspicious MBR at sector 0
gpt add: /dev/disk0: error: no space available on device


This is the output from sudo gpt -r show /dev/disk0

   gpt show: /dev/disk0: Suspicious MBR at sector 0
     start       size  index  contents
         0          1         MBR
         1          1         Pri GPT header
         2         32         Pri GPT table
        34          6         
        40     409600      1  GPT part - C12A7328-F81F-11D2-BA4B-00A0C93EC93B
    409640  776617328      2  MBR part 218
 777026968    1269760      3  GPT part - 48465300-0000-11AA-AA11-00306543ECAC
 778296728        616         
 778297344  198807552      4  MBR part 175
 977104896        131         
 977105027         32         Sec GPT table
 977105059          1         Sec GPT header


Progress:

I have executed command sudo gpt destroy /dev/disk0

But when I tried to add the first partition back using this command sudo gpt add -b 40 -s 409600 -i 1 -t C12A7328-F81F-11D2-BA4B-00A0C93EC93B /dev/disk0

I got this error straight away 

gpt add: /dev/disk0: Suspicious MBR at sector 0
gpt add: /dev/disk0: error: no primary GPT header; run create or recover


Now the command sudo gpt -r show /dev/disk0 gives me this

   gpt show: /dev/disk0: Suspicious MBR at sector 0
     start       size  index  contents
         0          1         MBR
         1     409639         
    409640  776617328      2  MBR part 218
 777026968    1269760      3  MBR part 175
 778296728        616         
 778297344  198807552      4  MBR part 175
 977104896        164


Progress 2:

I executed sudo gpt create /dev/disk0
and got this error:

gpt create: /dev/disk0: Suspicious MBR at sector 0
gpt create: /dev/disk0: error: device contains a MBR


and I executed this command sudo fdisk -i -a hfs /dev/disk0 to write new MBR
and executed sudo gpt create /dev/disk0 again but got the same error gpt create: /dev/disk0: error: device contains a MBR

Now sudo gpt -r show /dev/disk0 gives me this

      start       size  index  contents
      0          1         MBR
      1         62         
     63  977104997      1  MBR part 175


Progress 3 and final :D

Firstly a big thank to @klanomath, without the help, I couldn't go this far.

I executed this command sudo gpt create -fp /dev/disk0

And this command sudo gpt recover /dev/disk0 to get the secondary GPT header

After that, I executed sudo gdisk /dev/disk0 and the disk is mounted and functions properly
The content type of the second partition is wrong. Instead of FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFFFFFF it has to be 53746F72-6167-11AA-AA11-00306543ECAC.

To edit the content type you have to boot to Internet Recovery Mode and use gpt. Additionally the fourth partition will be removed (probably the "deleted" partition). Please check that it doesn't contain any data!

Preparation:


Detach any external drive (especially your external Time Machine backup drive)
Restart to Internet Recovery Mode by pressing alt cmd R at startup.

The prerequisites are the latest firmware update installed, either ethernet or WLAN (WPA/WPA2) and a router with DHCP activated.
On a 50 Mbps-line it takes about 4 min (presenting a small animated globe) to boot into a recovery netboot image which usually is loaded from an Apple/Akamai server.

I recommend ethernet because it's more reliable. If you are restricted to WIFI and the boot process fails, just restart your Mac until you succeed booting.

Alternatively you may start from a bootable installer thumb drive (preferably Yosemite or El Capitan) or a thumb drive containing a full system (preferably Yosemite or El Capitan). If you boot to a full system and login as admin you have to prepend sudo to execute special commands like gpt ...!


Remove the fourth partition and change the content type of the second partition


Booted to Internet Recovery Mode open Utilities → Terminal in the menubar and enter:  diskutil list to get the disk identifiers. Below I assume that your main disk has the disk identifiers disk0.
First you have to remove the fourth partition (only do that if it is really empty!):

gpt -r show /dev/disk0 #to get an overview


To delete a partition with gpt the disk has to be unmounted:

diskutil unmountDisk /dev/disk0
gpt remove -i 4 /dev/disk0 #remove the fourth partition

Then you have to change the content type of the second partition:

diskutil unmountDisk /dev/disk0
gpt remove -i 2 /dev/disk0 #remove the second partition
gpt add -b StartBlock -s NumberOfBlocks -i 2 -t 53746F72-6167-11AA-AA11-00306543ECAC


In your case:

gpt add -b 409640 -s 776617328 -i 2 -t 53746F72-6167-11AA-AA11-00306543ECAC /dev/disk0

Now you should be asked for the FileVault passphrase. Enter it.
Enter exit and quit Terminal
Check the main volume Macintosh HD for errors
Quit Disk Utility and reboot to your main volume




Addendum: Removing the stubborn MBR

You can either use fdisk or gpt to remove the MBR at block 0. If you use an admin user prepend sudo using the gpt .... commands.


First get an overview again. This step is important before you destroy the gpt, because it's the source to rebuild it from scratch:

gpt -r show /dev/disk0

Then delete the gpt:

diskutil unmountDisk /dev/disk0
gpt destroy /dev/disk0

Create a new GUID partition table:

gpt create -f /dev/disk0

Finally add all partitions one by one:

gpt add -b 40 -s 409600 -i 1 -t C12A7328-F81F-11D2-BA4B-00A0C93EC93B /dev/disk0
gpt add -b 777026968 -s 1269760 -i 3 -t 426F6F74-0000-11AA-AA11-00306543ECAC /dev/disk0
gpt add -b 409640 -s 776617328 -i 2 -t 53746F72-6167-11AA-AA11-00306543ECAC /dev/disk0


Hint: You may add and remove partitions in an arbitrary order if you keep the right index number. In the above commands I added the third partition (... -i 3 ...) before adding the second partition (... -i 2 ...). You don't have to unmount disk0 then because the partitions i=1 and i=3 don't contain auto-mounted volumes while the second partition does.

I missed to detect the wrong partition type of your Recovery HD (the third partition with the index number 3) in the first part of my answer. Therefore I used:

gpt add -b 777026968 -s 1269760 -i 3 -t 426F6F74-0000-11AA-AA11-00306543ECAC /dev/disk0


above instead of the wrong

gpt add -b 777026968 -s 1269760 -i 3 -t 48465300-0000-11AA-AA11-00306543ECAC /dev/disk0 #wrong partition type of the Recovery HD


to re-add it.

If you still get errors, tackle the MBR with fdisk. If you use an admin user prepend sudo using the fdisk ... commands.:

fdisk -i -a hfs /dev/disk0


and add the gpt entries with gpt ... outlined above.




Resizing the main volume to fill the whole disk

Finally you probably want to resize the main volume to fill the whole disk.


Get an overview with:

diskutil cs list


You may have several CoreStorage Logical Volume Groups, if you boot from an external drive with a full system! Use the proper one!
Resize the whole stack:

diskutil cs resizeStack lvUUID size #lvUUID is the UUID of the Logical Volume. Usually it's the last one listed.


Booted to Yosemite you can use 0g for the size to expand it. 0g is a "magical" size here.

diskutil cs resizeStack lvUUID 0g


Booted to El Capitan you have to use a real size like 500g. If you get an error use a slightly smaller size like 499g or499500m.

diskutil cs resizeStack lvUUID 500g