In the space below, algebraically solve the equation $\cos 3 x=0.5$ in the domain $-180^{\circ} \leq x \leq 360^{\circ}$

Step 1 ：Find the angles whose cosine is 0.5: \(\cos^{-1}(0.5) = 60^\circ, 300^\circ\)

Step 2 ：Divide the angles by 3 to get the values of x: \(x_1 = \frac{60^\circ}{3} = 20^\circ\), \(x_2 = \frac{300^\circ}{3} = 100^\circ\)

Step 3 ：\(\boxed{x = 20^\circ, 100^\circ}\)