Sum Of Tangent Squared?

Geometry Level 4

\[\large \sum_{r=0}^{89}\tan^2(r^\circ)\]

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

Clarification: Angles are measured in degrees.


This problem is part of my set: Geometry

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