If $5\cos 2\theta + 2{\cos ^2}\frac{\theta }{2} + 1 = 0, - \pi < \theta < \pi $, then $\theta = $

  • A

    $\frac{\pi }{3}$

  • B

    $\frac{\pi }{3},{\cos ^{ - 1}}\frac{3}{5}$

  • C

    ${\cos ^{ - 1}}\frac{3}{5}$

  • D

    $\frac{\pi }{3},\pi - {\cos ^{ - 1}}\frac{3}{5}$

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  • [JEE MAIN 2022]