Find all exact solutions on $[0,2 \pi)$. (Enter your answers as a comma-separated list.)
\[
2 \sin (3 \theta)=\sqrt{2}
\]

Step 1 ：Isolate \(\sin(3\theta)\) on one side of the equation by dividing both sides by 2. This gives us \(\sin(3\theta) = \frac{\sqrt{2}}{2}\).

Step 2 ：Find the values of \(\theta\) that satisfy this equation. We know that \(\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}\) and \(\sin(\frac{5\pi}{4}) = \frac{\sqrt{2}}{2}\), so \(3\theta = \frac{\pi}{4}\) and \(3\theta = \frac{5\pi}{4}\) are two possible solutions.

Step 3 ：Since the sine function has a period of \(2\pi\), we also need to consider solutions of the form \(3\theta = \frac{\pi}{4} + 2n\pi\) and \(3\theta = \frac{5\pi}{4} + 2n\pi\), where \(n\) is an integer.

Step 4 ：Divide each solution by 3 to solve for \(\theta\), and only keep the solutions that are in the interval \([0, 2\pi)\).

Step 5 ：The exact solutions on \([0,2 \pi)\) are \(\boxed{\frac{\pi}{12}, \frac{\pi}{4}, \frac{3\pi}{4}, \frac{11\pi}{12}, \frac{17\pi}{12}, \frac{19\pi}{12}}\).