If the minimum and the maximum values of the function $f : \left[ \frac { \pi } { 4 } , \frac { \pi } { 2 } \right] \rightarrow R$, defined by $f ( \theta ) = \left| \begin{array} { c c c } - \sin ^ { 2 } \theta & - 1 - \sin ^ { 2 } \theta & 1 \\ - \cos ^ { 2 } \theta & - 1 - \cos ^ { 2 } \theta & 1 \\ 12 & 10 & - 2 \end{array} \right|$ are $m$ and $M$ respectively, then the ordered pair $( \mathrm { m } , \mathrm { M } )$ is equal to :\\
(1) $( 0,2 \sqrt { 2 } )$\\
(2) $( - 4,0 )$\\
(3) $( - 4,4 )$\\
(4) $( 0,4 )$