Решите уравнение sinx=sin6x

Решите задачу:

$\sin x=\sin6x;\\ \sin x=2\sin3x\cos3x;\\ \sin3x=\sin(2x+x)=\sin2x\cos x+\sin x\cos2x=\\ =2\sin x\cos^2x+\sin x\cos 2x=\sin x(2\cos^2x+\cos2x);\\ \sin x=\sin x(2\cos^2x+cos2x)\cos3x;\\ \cos3x=\cos(2x+x)=\cos2x\cos x-\sin2x\sin x=\\ =\cos x\cos 2x-2\sin x\cos x\sin x=\cos x(\cos2x+1-2\sin x-1)=\\ =\cos x(2\cos2x-1)\\ 1=(2cos^2x-1+cos2x+1)\cos x(2\cos2x-1);\\ 1=\cos x(2\cos2x+1)(2\cos2x-1);\\ 1=\cos x(4\cos^22x-1);\\ 1=\cos x(4(2\cos^2x-1)^2-1);\\ 1=\cos x(16\cos^4x-16\cos^2x+4-1);\\ \cos x=t;\\$
$1=t(16t^4-16t^2+3);\\ 16t^5-16t^3+3t-1=0;\\$