Solve the equation cos x (2 sin x + square root of 3) (- square root of 2 cos x + 1) = 0 for 0<x<2 pi

I already did hte question but since it's for marks I want someone to tell me if I did it correctly or not. My answers for this question was:

pi/3, pi/2, 4pi/3, 3pi/2, 3pi/2 and 5pi/3

If anyone has time can they tell me if I'm correct or not... if not then I will post my process and hopefully you can spot where I went wrong.

Thanks