Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2007 / Paper 1 / Section A / 7

The double-angle identity for the sine factors the equation as $2\cos \theta (\sin \theta -\cos \theta )=0$. The first factor gives $\theta =\pi /2$ in the specified interval; the second gives $\tan \theta =1$ and hence $\theta =\pi /4$. ThusKeeping the first factor avoids losing the solution where division by $\cos \theta$ would be invalid.