Since $ 0 < x < \frac\pi2 $, then $ 0 < 2x < \pi $, and $ \sin 2x > 0 $. The minimum of $ f(x) $ occurs when $ \sin^2 2x $ is maximized, i.e., when $ \sin^2 2x = 1 $. This happens when $ 2x = \frac\pi2 \Rightarrow x = \frac\pi4 $. - Abu Waleed Tea