If the minimum and the maximum values of the function \(f:\left[\frac{\pi}{4}, \frac{\pi}{2}\right] \rightarrow R\), def…

If the minimum and the maximum values of the function \(f:\left[\frac{\pi}{4}, \frac{\pi}{2}\right] \rightarrow R\), defined by \(f(\theta)=\left|\begin{array}{ccc}-\sin ^2 \theta & -1-\sin ^2 \theta & 1 \\-\cos ^2 \theta & -1-\cos ^2 \theta & 1 \\12 & 10 & -2\end{array}\right|\)
are \(m\) and \(M\) respectively, then the ordered pair \((m, M)\) is equal to:

[JEE Main 2020, 5 Sep (Shift 1)]