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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