IrMO 2018 Problem 8

Let $M$ be the midpoint of side $BC$ of an equilateral triangle $ABC$ . The point $D$ is on $CA$ extended such that $A$ is between $D$ and $C$ . The point $E$ is on $AB$ extended such that $B$ is between $A$ and $E$ , and $|MD| = |ME|$ . The point $F$ is the intersection of $MD$ and $AB$ . Prove that $\angle BFM = \angle BME$ .