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 \(B\).

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