Let \(f(x)=\left|\begin{array}{ccc}1+\sin ^2 x & \cos ^2 x & \sin 2 x \\ \sin ^2 x & 1+\cos ^2 x & \sin …

Let \(f(x)=\left|\begin{array}{ccc}1+\sin ^2 x & \cos ^2 x & \sin 2 x \\ \sin ^2 x & 1+\cos ^2 x & \sin 2 x \\ \sin ^2 x & \cos ^2 x & 1+\sin 2 x\end{array}\right|\), \(x \in\left[\frac{\pi}{6}, \frac{\pi}{3}\right]\). If \(\alpha\) and \(\beta\) respectively are the maximum and the minimum values of \(f\), then

[JEE Main 2023, 1 Feb (Shift 1)]