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## Homework Statement

Find the solution of

2(cos x + cos 2x)+sin 2x(1+2cos x)=2 sin x in the interval [-pi, pi]

## The Attempt at a Solution

Simplifying:

2 (cos x- sin x)+ sin 2x +cos 2x +2sin 2x cos x=0

2 (cos x- sin x)+ sin 2x +cos 2x +sin 3x+sin x=0

cos 2x+2cos x+sin 2x-sin x+sin 3x=0

But now its difficult to convert into factors to apply zero prouct rule.