Question 437589
{{{2cos^2(theta) + cos(2theta) = 0}}}
<==> {{{2cos^2(theta) + 2cos^2(theta) - 1 = 0}}}
<==> {{{4cos^2(theta) = 1}}}
<==> {{{cos^2(theta) = 1/4}}}
==> {{{cos(theta) = -1/2}}}, or {{{cos(theta) = 1/2}}}
From the first equation, we get 240 degrees or 300 degrees.
From the 2nd equation we get 60 degrees or 120 degrees.
All solutions can described by the following:

{{{60^0 + n*180^0}}} or {{{120^0 + n*180^0}}}, where n varies over all the integers.