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If theta_1 and theta_2 be respectively the smallest

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, $2 \cot ^{2} \theta-\frac{5}{\sin \theta}+4=0$, then

$\int_{\theta_{1}}^{\theta_{2}} \cos ^{2} 3 \theta d \theta$ is equal to :

 

  1. $\frac{2 \pi}{3}$

  2. $\frac{\pi}{3}+\frac{1}{6}$

  3. $\frac{\pi}{9}$

  4. $\frac{\pi}{3}$


Correct Option: , 4

Solution:

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