Solve : `2 cos^(2)theta + sin theta le 2`, where `pi/2 le theta le (3pi)/2.`

Explanation

To solve the inequality \(2 \cos^2 \theta + \sin \theta \leq 2\) for \(\frac{\pi}{2} \leq \theta \leq \frac{3\pi}{2}\), we can follow these steps:

### Step 1: Rewrite the inequality
We start with the given inequality:
\[ 2 \cos^2 \theta + \sin \theta \leq 2 \]
Using the Pythagorean identity \(\sin^2 \theta + \cos^2 \theta = 1\), we can express \(\cos^2 \theta\) in terms of \(\sin \theta\):
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