Explanation:

- Given equation: \( 2 \cos^2 \theta + \sin \theta - 2 = 0 \).

- Use the identity \( \cos^2 \theta = 1 - \sin^2 \theta \).

- Substitute: \( 2(1 - \sin^2 \theta) + \sin \theta - 2 = 0 \).

- Simplify: \( 2 - 2 \sin^2 \theta + \sin \theta - 2 = 0 \).

- This simplifies to: \( -2 \sin^2 \theta + \sin \theta = 0 \).

- Factor: \( \sin \theta (1 - 2 \sin \theta) = 0 \).

- Solutions: \( \sin \theta = 0 \) or \( 1 - 2 \sin \theta = 0 \).

- \( \sin \theta = 0 \) yields no solution in \( 0 < \theta \leq \pi/2 \).

- \( 1 - 2 \sin \theta = 0 \) gives \( \sin \theta = \frac{1}{2} \).

- \( \theta = \frac{\pi}{6} \);

- Possible \( \theta \) value: \(\theta = \frac{\pi}{6}\), \(\sin \theta = \frac{1}{2}\).

- Correct Option: Option 1 - \(\frac{\pi}{6}\)