If  $f\left(\theta \right)=\left|\begin{array}{ccc}1+{\sin }^2\theta & {\cos }^2\theta & 4\sin 2\theta \\ {\sin }^2\theta & 1+{\cos }^2\theta & 4\sin 2\theta \\ {\sin }^2\theta & {\cos }^2\theta & 1+4\sin 2\theta \end{array}\right|$ then which of the following  is/are CORRECT?

If  $f\left(\theta \right)=0$  then values of  $\theta$  in  $[0,\pi ]$ are $\frac{7\pi }{12},\frac{11\pi }{12}$

$f\left(\theta \right)=k$  has atleast one solution if  $k\in [-2,6]$

If  $f\left(\theta \right)=2$ then number of values of  $\theta$ in  $[0,2\pi ]$ is ‘5’

maximum value of  $f\left(\theta \right)$ is ‘6’