Let $f(x)=\left|\begin{array}{ccc}\sin ^2 x & -2+\cos ^2 x & \cos 2 x \\ 2+\sin ^2 x & \cos ^2 x & \cos 2 x \\ \sin ^2 x & \cos ^2 x & 1+\cos 2 x\end{array}\right|, x \in[0, \pi]$. Then the maximum value of $f(x)$ is equal to
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