Stuck on FileVault login screen with never ending spinner
TLDR: I contacted Apple about this problem, and they recommended to reinstall OS X, which seems like a temp fix.



Reinstalling OS X should at least allow you to login again. This is great if you have any data that isn't backed up. However, after a subsequent restart, I have experienced this problem again, so it seems like this only a temporary solution. 


Restart the computer. 
Hold command-c while it is starting up. 
Open Disk Utility.
Select the grayed out encrypted partition. 
Choose unlock.
Type in your FileVault master password. (You saved it somewhere safe, right?)
Close Disk Utility. 
Choose reinstall OS X. 
Go through the setup process. 
Once it is done, you should be able to login and access all of your data.


Note: according to the Apple representative, reinstalling OS X this way does not get rid of any of the data on your hard drive.