If  ${\sin }^{3}x.\sin 3x=\sum _{m=0}^n{C}_m\cos mx$  where  ${C_{\text{}}}_0,C_1,\mathrm{.........}{C}_n$ are constants and  $C_n\ne 0$ then m =

$$\begin{gathered} {\sin }^{3}x\sin 3x=c_0\cos 0^o+c_1\cos x+c_2\cos 2x+\mathrm{...}+c_n\cos nx \\ \left(\frac{3\sin x-\sin 3x}{4}\right)\sin 3x=c_0+c_1\cos x+c_2\cos 2x+\mathrm{...}+c_n\cos nx \\ \frac{3}{8}\left[2\sin 3x\sin x\right]-\frac{1}{4}{\sin }^{2}3x=c_0+c_1\cos x+c_2\cos 2x+\mathrm{...}\Rightarrow n=6 \end{gathered}$$