trigonometric eq

are u sure this is the right question.. i think you have made some mistake somewher.

\\let \pi/7=x \\7x=\pi \\4x=\pi-3x \\sin 4x = sin 3x \\4 sin x cos x cos 2x = 3 sinx - 4 sin^3x \\4 cos x cos 2x = 3- 4 sin^2x \\4 cos x cos 2x = 1 +2(1- 2 sin^2x) \\4 cos x cos 2x = 1 +2 cos 2x

Yup there is no mistake :P my wrong.