2. Let $\theta$ be the largest interior angle of a triangle, and satisfies $\sin 8 \theta=\sin 2 \theta$. Then the set of possible values of $\theta$ is $\qquad$ (express using the roster method).
2. $\left\{\frac{\pi}{3}, \frac{2 \pi}{3}, \frac{\pi}{2}, \frac{7 \pi}{10}, \frac{9 \pi}{10}\right\}$.

From $\sin 8 \theta=\sin 2 \theta$, we get
$8 \theta=2 k \pi+2 \theta$ or $8 \theta=(2 k+1) \pi-2 \theta$,
which means $\theta=\frac{1}{3} k \pi$ or $\theta=\frac{1}{10}(2 k+1) \pi$, where $k \in \mathbf{Z}$.
Since $\theta$ is the largest interior angle of a triangle, then $\frac{\pi}{3} \leqslant \theta<\pi$.
Therefore, the set of possible values of $\theta$ is
$$
\left\{\frac{\pi}{3}, \frac{2 \pi}{3}, \frac{\pi}{2}, \frac{7 \pi}{10}, \frac{9 \pi}{10}\right\} .
$$