# The value of $\theta$ in the first quadrant satisfying the equation $\begin{vmatrix}1+\cos^2\theta&\sin^2\theta&4\sin 4\theta\\\cos^2\theta&1+\sin^2\theta&4\sin4\theta\\\cos^2\theta&\sin^2\theta&1+4\sin 4\theta\end{vmatrix}=0$ is
$\begin{array}{1 1}(A)\;\large\frac{5\pi}{24}&(B)\;\large\frac{7\pi}{24},\frac{5\pi}{24}\\(C)\;\large\frac{\pi}{24}&(D)\;\large\frac{11\pi}{6},\frac{7\pi}{6}\end{array}$