Let  $P={\tan }^2\frac{\pi }{16}+{\tan }^2\frac{2\pi }{16}+{\tan }^2\frac{3\pi }{16}+{\tan }^2\frac{5\pi }{16}+{\tan }^2\frac{6\pi }{16}+{\tan }^2\frac{7\pi }{16}$, then which of the following is/are TRUE?

$$\begin{gathered} {\tan }^2\frac{7\pi }{16}={\cot }^2\frac{\pi }{16} and {\tan }^2\frac{6\pi }{16}={\cot }^2\frac{2\pi }{16},{\tan }^2\frac{5\pi }{16}={\cot }^2\frac{3\pi }{16} and \\ {\tan }^2\theta +{\cot }^2\theta ={(\tan \theta +\cot \theta )}^2-2=\frac{8}{1-\cos 4\theta }-2 \end{gathered}$$

Put,  $\theta =\frac{\pi }{16},\frac{2\pi }{16},\frac{3\pi }{16}$

$({\tan }^2\frac{\pi }{16}+{\tan }^2\frac{7\pi }{16})+({\tan }^2\left(\frac{2\pi }{16}\right)+{\tan }^2\left(\frac{6\pi }{16}\right))+({\tan }^2\frac{3\pi }{16}+{\tan }^2\frac{5\pi }{16})=34$