I encountered this problem earlier and couldn't figure out how to solve it. I couldn't get all that far with the problem. The red marks were added by me, couldn't figure out anything other than those little details.
Can you guys help me with this? What am I missing?
Hint: $ABCD$ is cyclic and so $\angle ADE + \angle DEA = \angle DCB$. But $\angle FEC$ is not determined by the given information.