If \(\tan 2\theta \cdot \tan 3\theta = 1\), then find the value of \(\theta\), given that \(0 \leq \theta \leq \cfrac{\pi}{2}\).

Q.If \(\tan 2\theta \cdot \tan 3\theta = 1\), then find the value of \(\theta\), given that \(0 \leq \theta \leq \cfrac{\pi}{2}\).

\(\tan 2\theta \cdot \tan 3\theta = 1\) Or, \(\tan 2\theta = \cfrac{1}{\tan 3\theta}\) Or, \(\tan 2\theta = \cot 3\theta\) Or, \(\tan 2\theta = \tan(90^\circ - 3\theta)\) Or, \(2\theta = 90^\circ - 3\theta\) Or, \(2\theta + 3\theta = 90^\circ\) Or, \(5\theta = 90^\circ\) Therefore, \(\theta = 18^\circ\) (Answer)