If \( \theta_{1} \) and \( \theta_{2} \) be respectively the smallest and the largest values of \( \theta \) in \((0,2\p…

If \( \theta_{1} \) and \( \theta_{2} \) be respectively the smallest and the largest values of \( \theta \) in \((0,2\pi )-\left{\pi \right}\) which satisfy the equation, \( 2 \cot ^{2} \theta-\frac{5}{\sin \theta}+4=0 \), then \(\int_{\theta_{1}}^{\theta_{2}} \cos ^{2} 3 \theta \mathrm{d} \theta \) is equal to: