Find all angles, $0^{\circ} \leq \theta<360^{\circ}$, that satisfy the equation below, to the nearest 1oth of a degree. \[ \sin (\theta)=-\frac{\sqrt{6}}{3} \]

Step 1 ：Find the reference angle in the first quadrant: \(\sin^{-1}\left(-\frac{\sqrt{6}}{3}\right) \approx 54.7^\circ\)

Step 2 ：Find the corresponding angles in the third and fourth quadrants: \(180^\circ + 54.7^\circ = 234.7^\circ\) and \(360^\circ - 54.7^\circ = 305.3^\circ\)

Step 3 ：\boxed{234.7^\circ, 305.3^\circ}