CN-TST 2012 Problem 13

In an acute-angled $ABC$ , $\angle A>60^{\circ}$ , $H$ is its orthocenter. $M,N$ are two points on $AB,AC$ respectively, such that $\angle HMB=\angle HNC=60^{\circ}$ . Let $O$ be the circumcenter of triangle $HMN$ . $D$ is a point on the same side with $A$ of $BC$ such that $\triangle DBC$ is an equilateral triangle. Prove that $H,O,D$ are collinear.