Day 7: Seven Terms in a Tricky Trig Sum
Geometry
Level
5
Solve: \[2\sin\theta(\sin2\theta +\sin4\theta +\sin6\theta +\dots+\sin14\theta ) = \cos\theta - \frac12\] where \(0^{\circ}\leq \theta \leq 24^{\circ}\).
Give your answer as the product of your solutions (each in degrees).
This problem is part of the Advent Calendar 2015.
by
Michael Ng