If $ \sin B=3 \sin (2A+B)$, prove that $2\tan A+\tan (A+B)=0$ 
Given $\sin B=3\sin(2A+B)$, prove $ 2\tan A+\tan(A+B)=0$.

My book uses componendo and dividendo approach to do this which I feel is bit unintuitive. I tried to do this by using identity for $\sin(x+y)=\sin x\cos y+\cos x\sin y$ but could not reach to answer. How do I do this?

I think using identity. Its become more difficult to solve. So you should have to use componendo and dividendo.
