Problem starting Music app on iPhone
The picture you're seeing is actually the page for Apple Music, it comes once you've updated the iOS to a relatively newer version supporting Apple Music. To get rid of that and proceed to your music library firstly make sure the phone is connected to the internet. Then open your music app. Once it's open at the bottom you should see a line saying either "No,Thanks" or "Continue to Music Library". 
Just click on either one. 
That did the trick for me when i faced this problem.