a)$ -\sin3x +2\sin^2 \frac{3x}{2}+2 \sin2x =0$
b) $ \sin^6 x+\cos^6 x =\frac{-7}{16} \tan \left(x-\frac{\pi}{3}\right) \tan \left(x+\frac{\pi}6\right)$
c) $\sin \left(7x-\frac{5\pi}6\right)+\cos \left(3x-\frac{\pi}3\right)=0$
d) $ \sin (\pi \cos x) =1$