Find all angles $\theta$ between $0^{\circ}$ and $180^{\circ}$ satisfying the given equation. (Enter your answers as a comma-separated list.) \[ \begin{array}{r} \cos (\theta)=\frac{\sqrt{3}}{2} \\ \theta=\square . \end{array} \]

Step 1 ：We are given the equation \(\cos (\theta)=\frac{\sqrt{3}}{2}\) and asked to find all angles \(\theta\) between \(0^{\circ}\) and \(180^{\circ}\) that satisfy this equation.

Step 2 ：The cosine function has a value of \(\frac{\sqrt{3}}{2}\) at two angles in the interval \(0^{\circ}\) to \(180^{\circ}\), namely \(30^{\circ}\) and \(150^{\circ}\).

Step 3 ：This is because the cosine function is positive in the first and fourth quadrants of the unit circle, and the reference angle associated with \(\frac{\sqrt{3}}{2}\) is \(30^{\circ}\).

Step 4 ：In the interval \(0^{\circ}\) to \(180^{\circ}\), these correspond to the angles \(30^{\circ}\) and \(180^{\circ}-30^{\circ}=150^{\circ}\).

Step 5 ：Final Answer: \(\theta=\boxed{30^{\circ}, 150^{\circ}}\)