$\int \frac{\sin \theta .\sin 2\theta ({\sin }^6\theta +{\sin }^4\theta +{\sin }^2\theta )\sqrt{2{\sin }^4\theta +3{\sin }^2\theta +6}}{1-\cos 2\theta }d\theta is$

$$\begin{gathered} \int \frac{\sin \theta .\sin 2\theta ({\sin }^6\theta +{\sin }^4\theta +{\sin }^2\theta )\sqrt{2{\sin }^4\theta +3{\sin }^2\theta +6}}{1-\cos 2\theta }d\theta \\ \int \frac{2{\sin }^2\theta \cos \theta ({\sin }^6\theta +{\sin }^4\theta +{\sin }^2\theta )\sqrt{2{\sin }^4\theta +3{\sin }^2\theta +6}}{2{\sin }^2\theta }d\theta \\ \begin{array}{l}put\sin \theta =t\\ \cos \theta d\theta =dt\end{array} \\ \int (t^6+t^4+t^2)\sqrt{2t^4+3t^2+6}dt \\ \int (t^5+t^3+t^1)\sqrt{2t^6+3t^4+6t^2}dt \\ 2t^6+3t^4+6t^2=y \end{gathered}$$