If θ_1 and θ_2 be respectively the smallest and the largest values of θ in (0,2 π)-{π} which satisfy the equation, 2 cot^2 θ-5/(sin θ)+4=0, then…

If $\displaystyle \theta_1$ and $\displaystyle \theta_2$ be respectively the smallest and the largest values of $\displaystyle \theta$ in $\displaystyle (0,2 \pi)-\{\pi\}$ which satisfy the equation, $\displaystyle 2 \cot ^2 \theta-\frac{5}{\sin \theta}+4=0, \quad$ then $\displaystyle \int_{\theta_1}^{\theta_2} \cos ^2 3 \theta \mathrm{~d} \theta$ is equal to :