Statement-I: For $n\in Z, 2{\sin }^2\theta = \cos 2\theta \Rightarrow \frac{\theta }{2}=\frac{n\pi }{2}\pm \frac{\pi }{12}$
Statement-II:  For $n\in Z, \tan 5x=cot3x\Rightarrow x = (2n+1)\frac{\pi }{4}$
which of the above statement is correct?

$$\begin{gathered} \mathrm{S}-\mathrm{I} : \\ 2{\sin }^2\mathrm{\theta }=\cos 2\mathrm{\theta } \\ 2{\sin }^2\mathrm{\theta }=1-2{\sin }^2\mathrm{\theta } \\ 4{\sin }^2\mathrm{\theta }=1 \\ {\sin }^2\mathrm{\theta }={\left(\frac{1}{2}\right)}^2={\sin }^2\frac{\mathrm{\pi }}{6} \\ \mathrm{\theta }=\mathrm{n\pi }\pm \frac{\mathrm{\pi }}{6} \end{gathered}$$

$$\begin{gathered} \mathrm{S}-\mathrm{II} : \\ \tan 5\mathrm{x}=\cot 3\mathrm{x} \\ \tan 5\mathrm{x}=\tan \left(\frac{\mathrm{\pi }}{2}-3\mathrm{x}\right) \\ 5\mathrm{x}=\mathrm{n\pi }+\frac{\mathrm{\pi }}{2}-3\mathrm{x} \\ 8\mathrm{x}=(2\mathrm{n}+1)\frac{\mathrm{\pi }}{2} \\ \mathrm{x}=(2\mathrm{n}+1)\frac{\mathrm{\pi }}{16} \end{gathered}$$