Determine the values of \(\theta\) for which \(\sin^2\theta - 3\sin\theta + 2 = 0\) holds true, given that \(0^\circ < \theta < 90^\circ\).

Q.Determine the values of \(\theta\) for which \(\sin^2\theta - 3\sin\theta + 2 = 0\) holds true, given that \(0^\circ < \theta < 90^\circ\).

\(\sin^2\theta - 3\sin\theta + 2 = 0\)
Or, \(\sin^2\theta - 2\sin\theta - \sin\theta + 2 = 0\)
Or, \(\sin\theta(\sin\theta - 2) - (\sin\theta - 2) = 0\)
Or, \((\sin\theta - 2)(\sin\theta - 1) = 0\)

Either \((\sin\theta - 1) = 0\) \(\therefore \sin\theta = 1\)
Or, \((\sin\theta - 2) = 0\) \(\therefore \sin\theta = 2\)
Since the value of \(\sin \theta\) cannot be greater than \(1\), we conclude that \(\sin\theta = 1\), therefore \(\theta = 90^\circ\).