Solve for the exact solutions in the interval [0,2π)\displaystyle {\left[{0},{2}\pi\right)}[0,2π). 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}}cos(2x)cos(x)−sin(2x)sin(x)=−23
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