# Sum of Sines is a Tangent?

Geometry Level 4

$\displaystyle\sum_{k=1}^{35}\sin (5k)=\tan \left ( \dfrac mn \right )$

If $$m,n$$ are coprime positive integers, with $$\frac m n < 90$$, find $$m+n$$.

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Details and Assumptions

• Angles are measured in degrees.
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