Solve for the exact solutions in the interval [0,2π)\displaystyle {\left[{0},{2}\pi\right)}. If the equation has no solutions, respond with DNE.

 cos(2x)cos(x)sin(2x)sin(x)=32\displaystyle {\cos{{\left({2}{x}\right)}}}{\cos{{\left({x}\right)}}}-{\sin{{\left({2}{x}\right)}}}{\sin{{\left({x}\right)}}}=-\frac{\sqrt{{{3}}}}{{2}}