TITLE: Are there any constants other than $\pi$ that give rational or known irrational values for $\cos(\theta)$?
QUESTION [5 upvotes]: For example: 
$\cos(\frac{\pi}{3}) = \frac{1}{2}$
$\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ 
Is there any other constant $\theta$ such that $\cos(k\theta)$ is rational or a known irrational where $k$ is not $0$ or something trivial like $\frac{\pi}{\theta}$?

REPLY [5 votes]: Here is a reasonable reference:
http://en.wikipedia.org/wiki/Exact_trigonometric_constants
To quote:
"According to Niven's theorem, the only rational values of the sine function for which the argument is a rational number of degrees are 0, 1/2, and 1."
Doing a search for
"rational values of cosine"
produced this result 
and many other useful references.