MathNet 2013 Question 20

The right prism $ABCA'B'C'$, with $AB = AC = BC = a$, has the property that there exists a unique point $M \in (BB')$ so that $AM \perp MC'$. Find the measure of the angle of the straight line $AM$ and the plane $(ACC')$.
Mircea Fianu, Cristian Mangra