Given 

$\cos(\pi/4 + 2\pi/3)$ 

and 

$\cos(\pi/4 + 4\pi/3)$

I wish to show that these values are given by $(\pm(\sqrt{6}) - \sqrt{2})/4$.

What is a quick way to arrive at these exact solutions (perhaps even by inspection)?

*I am currently using the addition of cosine formula, but it is too slow. I'm thinking perhaps a graphic method can be used?*