Find all solutions to $2 \sin (\theta)=-\sqrt{3}$ on the interval $0 \leq \theta<2 \pi$ \[ \theta= \] Give your answers as exact values, as a list separated by commas. Question Help: $\square$ Video 1 Video 2 Calculator Submit Question

Step 1 ：Given the equation is \(2 \sin (\theta)=-\sqrt{3}\). We need to find all solutions for \(\theta\) in the interval \(0 \leq \theta<2 \pi\).

Step 2 ：Simplify the equation to \(\sin (\theta)=-\frac{\sqrt{3}}{2}\).

Step 3 ：\(\sin (\theta)\) is negative in the third and fourth quadrants.

Step 4 ：The reference angle for \(\frac{\sqrt{3}}{2}\) is \(\frac{\pi}{3}\) or \(60^\circ\).

Step 5 ：The solutions in the third and fourth quadrants would be \(\pi + \frac{\pi}{3}\) and \(2\pi - \frac{\pi}{3}\) respectively.

Step 6 ：The exact values of \(\theta\) in the third and fourth quadrants would be \(\frac{4\pi}{3}\) and \(\frac{5\pi}{3}\) respectively.

Step 7 ：The solutions to \(2 \sin (\theta)=-\sqrt{3}\) on the interval \(0 \leq \theta<2 \pi\) are \(\theta=\boxed{\frac{4\pi}{3}, \frac{5\pi}{3}}\).