نکته: $\left\{ \begin{matrix} \operatorname{Sin}(\alpha +\beta )=\operatorname{Sin}\alpha \operatorname{Cos}\beta +\operatorname{Sin}\beta \operatorname {Cos}\alpha   \\ \operatorname{Sin}(\alpha -\beta )=\operatorname{Sin}\alpha \operatorname{Cos}\beta -\operatorname{Sin}\beta \operatorname {Cos}\alpha   \\ \end{matrix} \right.$ با توجه به نکته داریم: $\operatorname{Sin}2\alpha \operatorname{Cos}4\alpha =\operatorname{Sin}4\alpha \operatorname{Cos}2\alpha +\frac{1}{3}\Rightarrow \operatorname{Sin}4\alpha \operatorname{Cos}2\alpha -\operatorname{Sin}2\alpha \operatorname{Cos}4\alpha =-\frac{1}{3}\Rightarrow \operatorname{Sin}(4\alpha -2\alpha )=-\frac{1}{3}\Rightarrow \operatorname{Sin}(2\alpha )=-\frac{1}{3}$