The value of $\theta $ lying between $0$ and $\pi /2$ and satisfying the equation

$\left| {\,\begin{array}{*{20}{c}}{1 + {{\sin }^2}\theta }&{{{\cos }^2}\theta }&{4\sin 4\theta }\\{{{\sin }^2}\theta }&{1 + {{\cos }^2}\theta }&{4\sin 4\theta }\\{{{\sin }^2}\theta }&{{{\cos }^2}\theta }&{1 + 4\sin 4\theta }\end{array}\,} \right| = 0$

  • [IIT 1988]
  • A

    $\frac{{7\pi }}{{24}}$ or $\frac{{11\pi }}{{24}}$

  • B

    $\frac{{5\pi }}{{24}}$

  • C

    $\frac{\pi }{{24}}$

  • D

    None of these

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  • [IIT 2013]

If $2(\sin x - \cos 2x) - \sin 2x(1 + 2\sin x)2\cos x = 0$ then