Question 37
In a triangle $ABC$ we have $|AB| = 2|AC|$. Let $D$ and $E$ be the two points on the segments $AB$ and $BC$, such that $\angle BAE = \angle ACD$. The segments $AE$ and $CD$ intersect at $F$, and $CFE$ is an equilateral triangle. Find the angles of the triangle $ABC$.