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Geometry Level 4

A straight pillar PQPQ stands at a point PP, the points AA and BB are situated due south and east of PP respectively. MM is the mid-point of ABAB. PAMPAM is an equilateral triangle and NN is the foot of the perpendicular from PP on ABAB. Suppose AN=20 metersAN = 20 \text{ meters} and the angle of elevation of the top of the pillar at NN is tan1(2) \tan^{-1} (2) . Find the sum of the angles of elevation of its top at AA and BB.

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Inspired by IIT 1990 Question.
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