Answer
$\frac{4\pi}{27},\frac{22\pi}{27},\frac{40\pi}{27}$
Work Step by Step
Using trigonometric identities, we have
$sin(3\theta+\frac{\pi}{18})=1 \longrightarrow 3\theta+\frac{\pi}{18}=\frac{\pi}{2}, \frac{5\pi}{2}, \frac{9\pi}{2} \longrightarrow \theta=\frac{4\pi}{27},\frac{22\pi}{27},\frac{40\pi}{27}$