Sum Of Tangent Squared?

Geometry Level 4

r=089tan2(r)\large \sum_{r=0}^{89}\tan^2(r^\circ)

If the value of the above summation can be expressed as pq\dfrac{p}{q}, where pp and qq are coprime positive integers, find p+qp+q

Clarification: Angles are measured in degrees.

This problem is part of my set: Geometry


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