Exercise 4.3 - Inscribed equilateral triangle
The triangles ABD and ABC are equilateral, hence the angle ABE is 120°.
The angle ADF is 120°, too, since ADB is 60°.
Moreover the angles AFB and AEF are congruent, since they insist on the same arc. Finally AD is congruent to AB, so the triangles ADF and AEB are congruent, so AE is congruent to AF.
By construction the angle FBE is 60°, so also EAF is 60°, since they insist upon the same arc. So also the angles AEF and AFE are 60°