How to save data from broken GPT, GUID and unmountable, no type volumes? I have a Macbook Pro mid 2012 and 750GB hard drive. I tried to delete Windows partition on the hard disk and now I can't access my main Mac partition (disk index 2) anymore. It shows something like "FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFFFFFF" and I don't even know what it is.

I don't want to format/delete this partition because it has important files. The main Mac partition had FileVault enabled and this is the output from sudo gpt -r show disk0

 start        size  index  contents
           0           1         PMBR
           1           1         Pri GPT header
           2          32         Pri GPT table
          34           6         
          40      409600      1  GPT part - C12A7328-F81F-11D2-BA4B-00A0C93EC93B
      409640  1167843728      2  GPT part - FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFFFFFF
  1168253368        1608         
  1168254976   126689280      3  GPT part - 48465300-0000-11AA-AA11-00306543ECAC
  1294944256      262144         
  1295206400   168673192      4  GPT part - 53746F72-6167-11AA-AA11-00306543ECAC
  1463879592     1269536      5  GPT part - 426F6F74-0000-11AA-AA11-00306543ECAC
  1465149128           7         
  1465149135          32         Sec GPT table
  1465149167           1         Sec GPT header


I appreciate any help or suggestions!
I deleted from the MAC-Disk utility window. No, I am not trying to boot into OS X or trying to mount the disk from another system. I am just trying to save my files from that partition.

Here are the screens: 

diskutil list


diskutil cs list


Thanks!