Are there any constants other than $\pi$ that give rational or known irrational values for $\cos(\theta)$?

Question

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 $\frac{\pi}{\theta}$?

Answer 1

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.