Q: Under the Music tab there is no option to Sync Music!

Follow the instructions in the support article below that applies to your computer:

iTunes 12 for Windows: Sync iPod, iPhone, or iPad

iTunes 12 for Mac: Sync iPod, iPhone, or iPad

Cheers,

GB

The option to "Sync Only Checked Songs and Music" only controls what does not sync. If you do not have that option checked, then when you go to the Music tab on your device profile screen, you would select whatever specific albums, songs, playlists, or artists you wanted to sync. If some of the ones you had selected were not checked, and you had the "Sync Only Checked...." option on, they would not sync....

Cheers,

GB

try turning off iCloud music library you can do this by, (on phone) go to settings music turn off iCloud music library. On computer open iTunes, in the very top where it says iTunes click preferences general and uncheck iCloud music library.

Another thing you can try is, in preferences go to sharing if sync with wi-fi click share selected playlists then click on the things that you want to share then click share entire library again. then try to sync it should work.

This post was made prior to the introduction of Apple Music, so the recommendations you have listed do not pertain to the issue the OP was describing.

Cheers,

GB