Solve the following equation:
$4 {sin}^{4} x + {sin}^{2} 2 x = 1$

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Solution

${4 sin}^{4} x + {4 sin}^{2} x {cos}^{2} x = 1$
$4 ({sin}^{4} x + {sin}^{2} - {sin}^{4} x) = 1$
$sin x = \pm \frac{1}{2}$
$x = n π \pm {(- 1)}^{n} \frac{π}{6} .$

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