$\sin x+2 \sin 2x=3+\sin 3x$ 

$\begin{array}{l}\sin x+2\sin 2x-\sin 3x=3\\ \Rightarrow \sin 3x\ge 0\Rightarrow 0\le 3x\le \pi \\ \Rightarrow 0\le x\le \pi /3\Rightarrow 0\le \sin x\le \sqrt{3}/2\\ \text{ and }0\le 2x\le 2\pi /3\Rightarrow 0\le \sin 2x\le 1\\ -1\le -\sin 3x\le 0\end{array}$

So $-1\le \sin x+\sin 2x-\sin 3x\le \sqrt{3/2+1<3}$

So the given equation is not satisfied for any real value of $x$