Solution
= Solution
The inequality is equivalent to $|\cos\theta|>1/\sqrt2$. The <cosine> exceeds $1/\sqrt2$ close to zero and $2\pi$, and is less than $-1/\sqrt2$ close to $\pi$. Within the specified interval this gives
$$
\boxed{\theta\in[0,\pi/4)\ \cup\ (3\pi/4,5\pi/4)\ \cup\ (7\pi/4,2\pi].}
$$
The four equality angles are excluded because the inequality is strict; zero and $2\pi$ satisfy it and are included.