Let M and N respectively be the maximum and the minimum values of $f(x) = \left| {\begin{array}{*{20}{c}} {1 + {{\sin }^2}x}&{{{\cos }^2}x}&{4\sin 4x}\\ {{{\sin }^2}x}&{1 + {{\cos }^2}x}&{4\sin 4x}\\ {{{\sin }^2}x}&{{{\cos }^2}x}&{1 + 4\sin 4x} \end{array}} \right|,x \in {\rm{R}}$
Then ${M^4} - {m^4}$ is equal to :