I've been seeing a number of people (including myself) being stuck in an iOS storm where we could not sign into our Apple ID after updating to iOS 9.3 betas.
I have a possible solution, it worked for me and might work for you.
Prerequisites: Backup if you haven't yet
1) Use iTunes to restore the iPhone to iOS 9.2.1.
2) Set up as new device
3) Download config file from the Resources page of the Developer site
4) Update your phone over the air.
5) Restore your backup!
My problem was iTunes. When using the .ipsw file downloaded from the member center, it created this verification bug. It seems that an OTA update doesn't do this, and I have no idea why.
Hope this helps!