Simplifying $ \cos(4\pi a)+\cos(4\pi b) + \cos(2\pi(a+b))\\ +\cos(2\pi(2a+b))+\cos(2\pi(a+2b))+\cos(4\pi(a+b)), $
Andrew Henderson 
Is it possible to simplify the following expression$$ \cos\left(4\pi a\right)+\cos\left(4\pi b\right) + \cos\left(2\pi\left(a+b\right)\right)\\ +\cos\left(2\pi\left(2a+b\right)\right)+\cos\left(2\pi\left(a+2b\right)\right)+\cos\left(4\pi\left(a+b\right)\right), $$where $a,b\in\mathbb{R}$?
I've played around with some trigonometric identities, but can't seem to find a good way to simplify it, if there's one at all.
$\endgroup$ 3 Reset to default
