if 0<x, y<\(\pi\) and cosx+cosy-cos(x y)=\(\frac{3}{2}\),Then sin x+cos y=?
\(\frac{1}{2}\)
\(\frac{1+\sqrt3}{2}\)
\(\frac{\sqrt3}{2}\)
\(\frac{1-\sqrt3}{2}\)

Let \( M \) and \( m \) respectively be the maximum and the minimum values of \( f(x) = \begin{vmatrix} 1 + \sin^2x & \cos^2x & 4\sin4x \\ \sin^2x & 1 + \cos^2x & 4\sin4x \\ \sin^2x & \cos^2x & 1 + 4\sin4x \end{vmatrix}, \quad x \in \mathbb{R} \) for \( x \in \mathbb{R} \). Then \( M^4 - m^4 \) is equal to:

