Day 7: Seven Terms in a Tricky Trig Sum

Geometry Level 5

Solve: 2sinθ(sin2θ+sin4θ+sin6θ++sin14θ)=cosθ122\sin\theta(\sin2\theta +\sin4\theta +\sin6\theta +\dots+\sin14\theta ) = \cos\theta - \frac12 where 0θ240^{\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.
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