MathNet 2007-part-01 — 187 problems (EN–VI) Question 41

Let $ABC$ be an acute angled triangle with $\angle BAC = 60^\circ$ and $AB \gt AC$. Let $I$ be the incenter, and $H$ the orthocenter of the triangle $ABC$. Prove that
$$
2 \angle AHI = 3 \angle ABC.
$$