Given that $\cos A + \cos B + \cos C = 0$ and $\sin A + \sin B + \sin C = 0$. If  $\cos A + \cos B + \cos C = 0$ and $\sin A + \sin B + \sin C = 0$. 
The value of $ \sin^3A+\sin^3B+\sin^3C$
What I can see here is that as $\sin A + \sin B + \sin C = 0$ hence $ \sin^3A+\sin^3B+\sin^3C=3\sin A \sin B\sin C$  but I am not able to achieve a constant value. Please give some hint.

Hint: If the centroid of a triangle coincides with it circumcenter, the triangle is equilateral.
Answer:  $\sin^3(A)+\sin^3(B)+\sin^3(C)=3\sin^3(A)-\frac{9}{4}\sin(A)=-\frac{3}{4}\sin(3A)$.
