The value of $\theta $lying between 0 and $\pi /2$and satisfying the equation $\begin{vmatrix} {1 + {{\sin }^2}\theta }&{{{\cos }^2}\theta }&{4\sin 4\theta }\\ {{{\sin }^2}\theta }&{1 + {{\cos }^2}\theta }&{4\sin 4\theta }\\ {{{\sin }^2}\theta }&{{{\cos }^2}\theta }&{1 + 4\sin 4\theta } \end{vmatrix} =0$