JEE Math Practice Question

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

1. A.$$\left( {0,2\sqrt 2 } \right)$$
2. B.(-4, 0)
3. C.(-4, 4)
4. D.(0, 4)