Answer: -2pi/3, 4pi/3
Explanation:
Assuming you want answers on the interval [-2pi, 2pi].
since cos²(x/2+pi/3) = 1, we have two cases:
cos(x/2+pi/3) = 1
cos(x/2+pi/3) = -1
First, we know if cos(x) = 1, x=0 on the interval [0,2pi). So, x/2+pi/3 = 0 --> x = -2pi/3
Second, we know if cos(x) = -1, x=pi on the interval [0, 2pi). so, x/2+pi/3 = -1 makes x = 4pi/3
Hope this helped!