Question 42
In the triangle $ABC$ let $D$ be the foot of the altitude to the side $AB$. Given the points $E$ and $F$ on the sides $AD$ and $BC$, such that $\angle BAF = \angle ACE$, let the segments $AF$ and $CE$ intersect at $G$ and let the segments $AF$ and $CD$ intersect at $T$. Find the angles of the triangle $ABC$, given that $CGF$ is an equilateral triangle and the triangle $AET$ is isosceles with the apex at $E$.