Finding the remaining angle in this triangle

Question

By chance I came across a question on another stackexchange site that involved finding all angles in a triangle. It was actually about drawing the triangle using a computer program, but since I need practice in solving triangle problems anyway, I thought I give it a go. The triangle given is:

(source)

I managed to find:

• $\alpha = 60°$
• $\beta = 75°$
• $\angle ADC = 15°$
• $\angle BFC = 45°$

Now, the only angle remaining is $\gamma$, but I can't figure out how to find it.

Answer 1

Hint:
Since $DE$ and $DF$ are both radii of the circle, then $\Delta DEF$ is isosceles.