Mac Pro & Apple TV 2 for computer audio Equipment &amp; OS:


Apple TV 2
Mac Pro (circa 2013 - the cylinder) 
MacOS Sierra Version 10.12.6
DAC (digital to analog converter, this only has USB and TOSLINK connections)
HDMI cable connects Mac Pro &amp; Apple TV
TOSLINK (digital optical) cable connects Apple TV to DAC


What I want to do...

I want to use the Apple TV to stream iTunes music from my MacPro to the DAC which then connects directly to powered speakers.

Previously I have connected an earlier Mac Pro (circa 2009) directly to the DAC via TOSLINK.  This worked GREAT!  The earlier Mac Pro had a TOSLINK output.  The new Mac Pro (2013) doesn't.

Prior to that I has streamed iTunes wirelessly to the Apple TV which in turn connected by TOSLINK to the DAC.  This worked GREAT too!  When I set up this solution I had a TV monitor available that connected by HDMI to the Apple TV.

Unfortunately, I have no other monitor or TV display available to connect to the Apple TV.



Problems

&lt;&lt; System Preferences >> &lt;&lt; Sound >>

If I go to &lt;&lt; System Preferences >> &lt;&lt; Sound >> and look to "Select a device for sound output" I don't see the Apple TV connection via the HDMI.  Note, the Apple TV via the HDMI doesn't show up as an input either.

I do see the Apple TV available for AirPlay, but when I select it a pop-up window appears asking me to: "Enter the AirPlay code for "Apple TV"

I assume the "AirPlay code" is not a "password" for the Apple TV (my Apple ID password doesn't work).  I think the pop-up window wants one of those 4 to 6 digit "codes" that pops up on the device to which one wants to connect.   

As I don't have a monitor connected to the Apple TV I don't have anything that can display the "AirPlay code". 

Seems like the HDMI connection to the Apple TV should get me something, but I can't think of a way to make the Apple TV display appear on the monitors connected to the Mac Pro;-(

Suggestions appreciated.



iTunes

I have similar problems in iTunes.  If I open iTunes and try to select an output device, I can select the Apple TV but the same pop-up window requesting the "AirPlay code" that I don't have a way to see appears.

Note: I have a 27" Apple Cinema Display, but it has not way to connect directly to the Apple TV.

Again, any suggestions much appreciated.



Footnote -- If I had a shorter distance between the Mac Pro &amp; the DAC I could use USB, but USB doesn't do well at distances beyond 20 feet.
Contrary to what you write, the 2013 Mac Pro actually has TOSLINK output. The jack connector for the analog output doubles as an optical connection for digitally transferring the sound signal to your DAC.

This means that you can just use the TOSLINK solution that worked well for you before. You'll need a mini-TOSLINK to TOSLINK cable.