First let me say that this is not originally my idea. I found it off the xda forums but I cant remember what thread it was on.
When you use the youtube app you cannot exit out of it or turn off the screen without it stopping the playback of the music. I never really cared too much until I noticed that some apps that would notify me and it would shut it down. Also its just annoying to not be able to multi task when you want to listen to a song or anything else.
Heres how to do it:
1. Download Maxathon browser
2. Hit the app button when your in the browser
3. Scroll over to the right when your in the pop up menu until you find UA
4. Change it to desktop
5. Then go to the same menu where you will find options and go to Browser settings
6. In that sub menu go to "Flash on Demand" and hit "always on"
7. Navigate to the youtube website and play your video of choice
8. Then hit the app button again and open another tab
Once your in that tab you can press the home button and go about your business and multitask your phone like it was made for