Day 7: Seven Terms in a Tricky Trig Sum

Geometry Level 5

Solve: 2sin⁡θ(sin⁡2θ+sin⁡4θ+sin⁡6θ+⋯+sin⁡14θ)=cos⁡θ−122\sin\theta(\sin2\theta +\sin4\theta +\sin6\theta +\dots+\sin14\theta ) = \cos\theta - \frac12 where 0∘≤θ≤24∘0^{\circ}\leq \theta \leq 24^{\circ}.

Give your answer as the product of your solutions (each in degrees).

This problem is part of the Advent Calendar 2015.
Michael Ng by Michael Ng
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