I have a OnePlus One running CyanogenMod 12.
I started using tasks within Business Calendar 2 PRO app heavily. They synchronize using google tasks. So I can see my tasks in google calendar. This works well with my Nexus 7 2013 tablet and PC and worked well with the phone too. The phone recently stop synchronizing correctly and does not want to work again.
Screenshot - Sync (Click to enlarge image)
I noticed that arrows stay present after trying to sync the Calendar. First they wiggle instead of turning awkwardly and end up staying there. The events get synced, the tasks not.
I also have a "Sound Search for Google Play" syncing problem, but I turned that one off for the reason so that it does not interfere.
I have no idea what to do. Once I had a similar problem with Google Keep and I managed to find a card that was causing some db problem on google site - I removed it and synchronized and it started working again. But I could not see anything interesting in the logs this time.