1. I've modified your sketch a little bit (see attachment).

2. Since the triangle ACE is isosceles. Let x denote the value of the angle at C then the exterior angle of the triangle at E must have the value 2x.

3. Since (circle of Thales!) the triangle CBD is isosceles. Therefore the angle has a value of x.

4. Take the greyed triangle. The sum of all interior angles of this triangle is:

Solve for x.