100 Followers Problem

Geometry Level 4

$\large \sum_{k=1}^{35} \sin \left(5k^\circ \right) = \tan \left(\frac {m}{n}\right)^\circ$.

The equation above holds true for coprime positive integers $$m$$ and $$n$$, where $$\dfrac {m}{n} < 90$$. Find $$m+n$$.

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