Given is a triangle $ABC$ and on its sides the triangles $ABM, BCN$ and $CAP$ are build such that $\angle AMB = 150^o$, $AM = MB$, $\angle CAP = \angle CBN = 30^o$, $\angle ACP = \angle BCN = 45^o$. Prove that the triangle $MNP$ is an equilateral triangle.