1.
Let mm and MM be respectively the minimum and maximum values of
cos2x1+sin2xsin2x1+cos2xsin2xsin2xcos2xsin2x1+sin2x\begin{vmatrix} \cos^{2}x & 1+\sin^{2}x & \sin2x \\ 1+\cos^{2}x & \sin^{2}x & \sin2x \\ \cos^{2}x & \sin^{2}x & 1+\sin2x \end{vmatrix}

Then the ordered pair (m,M)(m,M) is equal to: