$\cos 12°+\cos 84°+\cos 132°+\cos 156°=$

$=\left(\cos 12°+\cos 132°\right)+\left(\cos 84°+\cos 156°\right)$

$=2\cos \left(\frac{12+132}{2}\right).\cos \left(\frac{12-132}{2}\right)+2\cos \left(\frac{84+156}{2}\right).\cos \left(\frac{84-156}{2}\right)$

$=2\cos 72°.\cos 60°+2\cos 120°.\cos 36°$

$=2\cos 72.\frac{1}{2}+2\left(-\frac{1}{2}\right).\cos 36$

$=\cos 72°-\cos 36°=\sin 18°-\cos 36°$

$=\frac{\sqrt{5}-1}{4}-\frac{\sqrt{5}+1}{4}=-\frac{2}{4}=-\frac{1}{2}$