[latex] cos^{2} \frac{3}{2}x = \frac{1}{4} [/latex]

[latex]cos^{2} \frac{3}{2}x = \frac{1}{4} \\ 2 cos(3 x) + 1 = 0 \\ cos(3x) = - \frac{1}{2} \\ 3x = \frac{\pi }{3} n + 2 \pi n \\ x = \frac{\pi }{9} n + \frac{2\pi}{3} n[/latex]