# Give me a Name

Geometry Level 4

A straight pillar $$PQ$$ stands at a point $$P$$, the points $$A$$ and $$B$$ are situated due south and east of $$P$$ respectively. $$M$$ is the mid-point of $$AB$$. $$PAM$$ is an equilateral triangle and $$N$$ is the foot of the perpendicular from $$P$$ on $$AB$$. Suppose $$AN = 20 \text{ meters}$$ and the angle of elevation of the top of the pillar at $$N$$ is $$\tan^{-1} (2)$$. Find the sum of the angles of elevation of its top at $$A$$ and $$B$$.