Question 8
In the diagram below, $ABC$ is an equilateral triangle, where $M$ and $N$ are points on $AC$ and $BM$, respectively, such that $\angle ABM=15^\circ$ and $\angle BAN=30^\circ$. Let $P$ be the intersection point of the line $AN$ with the circumcircle of triangle $ABM$. Prove that $AN=NP$.
