The maximum value of \(f\left(x\right)=\left|\begin{matrix}{\sin }^{2}x & 1+{\cos }^{2}x & \cos 2x \\ 1+{\sin }^{2}x & {…

The maximum value of

\(f\left(x\right)=\left|\begin{matrix}{\sin }^{2}x & 1+{\cos }^{2}x & \cos 2x \\ 1+{\sin }^{2}x & {\cos }^{2}x & \cos 2x \\ {\sin }^{2}x & {\cos }^{2}x & \sin 2x\end{matrix}\right|,\)

\(x\in R\) is

[JEE Main 2021, 16 Mar (Shift 2)]