Question 60
In $\triangle ABC$ with $AB = 1$, let $D$ be a point on $AC$ such that $\angle ABD = \angle C$ and let $E$ be a point on $AB$ such that $BE = DE$. Let $H$ be a point on $DE$ such that $AH \perp DE$ and $M$ be the midpoint of $CD$. If $AH = 2 - \sqrt{3}$, find the size of $\angle AME$. (posed by Xiong Bin)
