cose c ^ 2 θ( ^ 2 θ - 3cos θ + 2) ≥ 1, if θ belongs to

\cos^{2} \theta - 3cos \theta + 2 \ge \dfrac{1}{{cosec}^{2}\theta} = \sin^{2} \theta$<br />$\cos^{2} \theta - 3cos \theta + 2 \ge 1 - \cos^{2} \theta$<br />$2\cos^{2} \theta - 3cos \theta + 1 \ge 0$<br />\left(2cos \theta - 1\right)\left(cos \theta - 1\right) \ge 0$
$⇒ cos \theta \le \dfrac{1}{2}$ or $cos \theta \ge 1$
So, $\theta \in \left(\dfrac{\pi}{3}, \dfrac{\pi}{2}\right)$ of the given intervals.