The sum of solutions of the equation cos\(\frac{cos\,x}{1+sin\,x}\)=|tan 2x|,x\(\in\)(\(-\frac{\pi}{2},\frac{\pi}{2}\))-(\(-\frac{\pi}{4},\frac{\pi}{4}\)) is:
\(-\frac{11\pi}{6}\)
\(\frac{\pi}{10}\)
\(-\frac{7\pi}{30}\)
\(-\frac{\pi}{15}\)
The correct answer is option (A) : \(-\frac{11\pi}{6}\)

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:

