\displaystyle = \sin^3 x + \frac{1}{8} \Big[ (\sqrt{3} \cos x - \sin x - \sqrt{3} \cos x - \sin x ) \big( (\sqrt{3} \cos x - \sin x)^2 +(\sqrt{3} \cos x - \sin x)(\sqrt{3} \cos x + \sin x) + (\sqrt{3} \cos x + \sin x)^2 \big) \Big] 