The maximum value of
$$
f(x)=\left|\begin{array}{ccc}
\sin ^2 & 1+\cos ^2 x & \cos 2 x \\
1+\sin ^2 x & \cos ^2 x & \cos 2 x \\
\sin ^2 x & \cos ^2 x & \sin 2 x
\end{array}\right|, x \in R
$$
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