نکته: $\operatorname{Sin}3x=3\operatorname{Sin}x-4{{\operatorname{Sin}}^{3}}x$ 

$\operatorname{Sin}x+\operatorname{Sin}2x+\operatorname{Sin}3x=0\Rightarrow \operatorname{Sin}x+2\operatorname{Sin}x\operatorname{Cos}x+3\operatorname{Sin}x-4{{\operatorname{Sin}}^{3}}x=0$

$\Rightarrow 4\operatorname{Sin}x+2\operatorname{Sin}x\operatorname{Cos}x-4{{\operatorname{Sin}}^{3}}x=0\Rightarrow 2\operatorname{Sin}x(2+\operatorname{Cos}x-2{{\operatorname{Sin}}^{2}}x)=0$

$\Rightarrow 2\operatorname{Sin}x(2(1-{{\operatorname{Sin}}^{2}}x)+\operatorname{Cos}x)=0\Rightarrow 2\operatorname{Sin}x(2{{\operatorname{Cos}}^{2}}x+\operatorname{Cos}x)=0\Rightarrow 2\operatorname{Sin}x\operatorname{Cos}x(2\operatorname{Cos}x+1)=0$

$\Rightarrow \operatorname{Sin}2x(2\operatorname{Cos}x+1)=0\Rightarrow \operatorname{Sin}2x=0*\operatorname{Cos}x=-\frac{1}{2}$ 

$_{\operatorname{Cos}x=-\frac{1}{2}=-\operatorname{Cos}\frac{\pi }{3}=\operatorname{Cos}(\pi -\frac{\pi }{3})\Rightarrow \operatorname{Cos}x=\operatorname{Cos}(\frac{2\pi }{3})\Rightarrow x=2k\pi \pm \frac{2\pi }{3}}^{\operatorname{Sin}2x=0\to 2x=k\pi \Rightarrow x=\frac{k\pi }{2}}$