CAPS 2016 Problem 6

Let $ABC$ be an acute-angled triangle with $AB < AC$ . Tangent to its circumcircle $\Omega$ at $A$ intersects the line $BC$ at $D$ . Let $G$ be the centroid of $\triangle ABC$ and let $AG$ meet $\Omega$ again at $H \neq A$ . Suppose the line $DG$ intersects the lines $AB$ and $AC$ at $E$ and $F$ , respectively. Prove that $\angle EHG = \angle GHF$ .(Slovakia)