Sum of Sines is a Tangent?

Geometry Level 4

k=135sin(5k)=tan(mn)\displaystyle\sum_{k=1}^{35}\sin (5k)=\tan \left ( \dfrac mn \right )

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

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Details and Assumptions

  • Angles are measured in degrees.
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