If $\theta $1 and $\theta $2 be respectively the smallest and the largest values of $\theta $ in (0, 2$\pi $) - {$\pi $} which satisfy the equation, 2cot2$\theta $ - ${5 \over {\sin \theta }}$ + 4 = 0, then $\int\limits_{{\theta _1}}^{{\theta _2}} {{{\cos }^2}3\theta d\theta } $ is equal to :

Question

If $\theta $₁ and $\theta $₂ be respectively the smallest and the largest values of $\theta $ in (0, 2$\pi $) - {$\pi $} which satisfy the equation,
2cot²$\theta $ - ${5 \over {\sin \theta }}$ + 4 = 0, then
$\int\limits_{{\theta _1}}^{{\theta _2}} {{{\cos }^2}3\theta d\theta } $ is equal to :

${\pi \over 9}$

${{2\pi } \over 3}$

${{\pi } \over 3}$

${\pi \over 3} + {1 \over 6}$

Solution

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