ILL 1985 Problem 56

Let $ABCD$ be a rhombus with angle $\angle A = 60^\circ$ . Let $E$ be a point, different from $D$ , on the line $AD$ . The lines $CE$ and $AB$ intersect at $F$ . The lines $DF$ and $BE$ intersect at $M$ . Determine the angle $\angle BMD$ as a function of the position of $E$ on $AD.$