Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2009 / Paper 2 / 9 / Solution

The inequality is equivalent to $|\cos \theta |>1/\sqrt{2}$. The cosine exceeds $1/\sqrt{2}$ close to zero and $2\pi$, and is less than $-1/\sqrt{2}$ close to $\pi$. Within the specified interval this givesThe four equality angles are excluded because the inequality is strict; zero and $2\pi$ satisfy it and are included.