Answer
The possible values are $\theta = \frac{\pi }{6}$ or $\theta = \frac{{5\pi }}{6}$.
Work Step by Step
From Theorem 1 the length of ${\bf{e}} \times {\bf{f}}$ is
$||{\bf{e}} \times {\bf{f}}|| = ||{\bf{e}}||||{\bf{f}}||\sin \theta $,
where $\theta$ is the angle between ${\bf{e}}$ and ${\bf{f}}$.
Since ${\bf{e}}$ and ${\bf{f}}$ are unit vectors, and $||{\bf{e}} \times {\bf{f}}|| = \frac{1}{2}$, it follows that
$||{\bf{e}} \times {\bf{f}}|| = ||{\bf{e}}||||{\bf{f}}||\sin \theta = \frac{1}{2}$
$\sin \theta = \frac{1}{2}$
By Theorem 1 the angle between ${\bf{e}}$ and ${\bf{f}}$ is $0 \le \theta \le \pi $. So, the possible values are $\theta = \frac{\pi }{6}$ or $\theta = \frac{{5\pi }}{6}$.
