MathNet 2011 Question 34

Let $VABC$ be a regular pyramid with the base $ABC$ having center $O$. Denote $I$ and $H$ the incenter and the orthocenter of the triangle $VBC$ and suppose that $AH = 3OI$. Find the measure of the angle made by a lateral edge of the pyramid with the plane of the base.
Mircea Fianu