# Summing sines

Geometry Level 4

Given that $$\displaystyle \sum_{k=1}^{35} \sin(5\cdot k^\circ)= \tan \left( \dfrac mn \right)$$, where $$m$$ and $$n$$ are coprime positive integers satisfying $$\dfrac mn < 90$$, find $$m+n$$.

Clarification: The angles are measured in degrees.

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