Trigonometrical equations Find the general solution of the equation $\sin x + \sin 2x + \sin 3x = 0$. I have started doing this problem by applying the formula of $\sin A + \sin B$ but couldn't generalise it. Please solve it for me.

HINT:

Using Prosthaphaeresis Formulas,

$$\sin x+\sin3x=2\sin\frac{3x+x}2\cos\frac{3x-x}2$$

We can also use $\sin x=\sin(2x-x),\sin3x=\sin(2x+x)$

Now $\sin y=0\implies y=n\pi$

and $\cos A=\cos B\implies A=2m\pi\pm B$ where $m,n$ are arbitrary integers