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 $m+n$ .