Find all angles, \( 0^{\circ} \leq \theta<360^{\circ} \), that solve the following equation. \[ \cos \theta=-\frac{\sqrt{3}}{2} \]

To solve the equation \(\cos \theta = -\frac{\sqrt{3}}{2}\), we first need to identify the angles where the cosine of an angle is negative. The cosine function is negative in the second and third quadrants. The reference angle associated with \(\cos \theta = \frac{\sqrt{3}}{2}\) is \(30^\circ\) (or \(\frac{\pi}{6}\) radians). Therefore, we need to find the angles corresponding to the reference angle in the second and third quadrants. 1. In the second quadrant: \[ \theta = 180^\circ - 30^\circ = 150^\circ \] 2. In the third quadrant: \[ \theta = 180^\circ + 30^\circ = 210^\circ \] Therefore, the solutions to the equation \(\cos \theta = -\frac{\sqrt{3}}{2}\) in the interval \(0^{\circ} \leq \theta < 360^{\circ}\) are: \[ \theta = 150^\circ, 210^\circ \]