Explanation: 
Another Explanation (5): ```html
Given, \(2\cos^2\theta - \sin\theta = 1\)
We know, \(\cos^2\theta = 1 - \sin^2\theta\)
So, \(2(1 - \sin^2\theta) - \sin\theta = 1\)
\(2 - 2\sin^2\theta - \sin\theta = 1\)
\(2\sin^2\theta + \sin\theta - 1 = 0\)
Let \(x = \sin\theta\)
\(2x^2 + x - 1 = 0\)
\(2x^2 + 2x - x - 1 = 0\)
\(2x(x+1) - 1(x+1) = 0\)
\((2x - 1)(x+1) = 0\)
So, \(2x-1=0\) or \(x+1=0\)
\(x = \frac{1}{2}\) or \(x = -1\)
Case 1: \(\sin\theta = \frac{1}{2}\)
\(\theta = \sin^{-1}(\frac{1}{2})\)
\(\theta = 30^\circ, 150^\circ\) 🥳🎉
Case 2: \(\sin\theta = -1\)
\(\theta = \sin^{-1}(-1)\)
\(\theta = 270^\circ\) ✨🎈
Therefore, the values of \(\theta\) are \(30^\circ\), \(150^\circ\), and \(270^\circ\). 😊👍
The answer "Both a and b" implies that there are two options, 'a' and 'b', which are both correct. Without knowing the specific options 'a' and 'b', we cannot definitively say which angles they represent. However, based on our calculation, possible options could be related to \(30^\circ\), \(150^\circ\), or \(270^\circ\). 🧐🤔
```
