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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