Answer
$\frac{4\pi}{27}, \frac{22\pi}{27}$
Work Step by Step
$sin(3\theta+\frac{\pi}{18})=1$,
$3\theta+\frac{\pi}{18}=2k\pi+\frac{\pi}{2}$
$\theta=\frac{2k\pi}{3}+\frac{4\pi}{27}$ (k is an integer),
$\theta=\frac{4\pi}{27}, \frac{22\pi}{27}$ in $[0,2\pi)$.
