Merci!
$\displaystyle \cos(2x)[2\cos{x} + 1] = 0$
set each factor equal to 0 ...
$\displaystyle \cos(2x) = 0$
$\displaystyle 2x = 90 \, , \, 270 \, , \, 450 \, , \, 630$
$\displaystyle x = 45 \, , \, 135 \, , \, 225 \, , \, 315$
$\displaystyle \cos{x} = -\frac{1}{2}$
$\displaystyle x = 120 \, , \, 240$