100 Followers Problem

Geometry Level 4

k=135sin(5k)=tan(mn)\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 mm and nn, where mn<90\dfrac {m}{n} < 90. Find m+nm+n.

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