If $ \cos x +2 \cos y+3 \cos z=0 , \sin x+2 \sin y+3 \sin z=0$ and $x+y+z=\pi$. Find $\sin 3x+8 \sin 3y+27 \sin 3z$ 
Problem : If $ \cos x +2 \cos y+3 \cos z=0 , \sin x+2 \sin y+3 \sin z=0$ and $x+y+z=\pi$. Find  $\sin 3x+8 \sin 3y+27 \sin 3z$
Solution: Adding $ \cos x +2 \cos y+3 \cos z=0$ and $\sin x+2 \sin y+3 \sin z=0$,we get
$ (\cos x+\sin x) +2(\cos y+\sin y)+3(\cos z+\sin z) =0$

Am I doing right ?

Hint: use complex exponentials. 
