Solving $2 \sin x \left( \sqrt{3} \cos x- \sin x \right)= \sqrt{2} - 1$ I wanted to know if this equation could be solved any further please.
$$2 \sin x \left( \sqrt{3} \cos x- \sin x \right)= \sqrt{2} - 1$$
I have gone this far:
$$4 \sin x \sin(60^\circ-x)= \sqrt{2}- 1$$
Thank you

Hint:
$$2\sqrt{3} \sin x  \cos x- 2\sin^2x = \sqrt3\sin 2x+\cos2x-1=\sqrt{2} - 1.$$
Then
$$3\sin^22x=3(1-\cos^22x)=(\sqrt2-\cos 2x)^2.$$
This is a quadratic equation in $\cos 2x$.
