What is $\left(1-{\sin }^2\theta \right)\left(1+{\tan }^2\theta \right)$ equal to$?$

Consider the following

$\mathrm{I}.$ $\tan \left(\frac{\pi }{6}\right)$

$\mathrm{II}.$ $\tan \left(\frac{3\pi }{4}\right)$

$\mathrm{III}.$ $\tan \left(\frac{5\pi }{4}\right)$

$\mathrm{IV}.$ $\tan \left(\frac{2\pi }{3}\right)$

Which one of the following is the correct order$?$

Consider the following statements

$\mathrm{I}.$ $\sin \left|x\right|+\cos \left|x\right|$ is always positive.

$\mathrm{II}.$ $\sin \left(x^2\right)+\cos \left(x^2\right)$ is always positive. 

Which of the above statement(s) is/are correct?