Find the exact solutions to cos(4x)cos(x)=−sin(4x)sin(x)\displaystyle {\cos{{\left({4}{x}\right)}}}{\cos{{\left({x}\right)}}}=-{\sin{{\left({4}{x}\right)}}}{\sin{{\left({x}\right)}}}cos(4x)cos(x)=−sin(4x)sin(x) in the interval [0,2π)\displaystyle {\left[{0},{2}\pi\right)}[0,2π). If the equation has no solutions, respond with DNE.
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