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