Summing Scattered Sines

Geometry Level 4

\[ \large \sin(\alpha) + \sin(3\alpha) + \sin(4\alpha) + \sin(5\alpha) + \sin(9\alpha) \]

Let \( \alpha = \dfrac{2\pi}{11} \), find the closed form of the expression above.

Give your answer to 3 decimal places.


Solving this numerically is a sin!
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