I know that if $x$ is a rational multiple of $\pi$, then $tan(x)$ is [algebraic](http://divisbyzero.com/2010/10/28/trigonometric-functions-and-rational-multiples-of-pi/).


Is there a fairly simple way to express $x$ as $\pi\ m/n$, if $tan(x)$ is given as a square root of a rational?



arctan of a square root as a rational multiple of pi
An angle $x$ with $\tan^2 x$ rational has been called "geodetic" by Conway, Radin, and Sadun, [On Angles Whose Squared Trigonometric Functions are Rational](http://arxiv.org/abs/math--ph/9812019). Geodetic angles have a simple representation, see their Theorem 2, but they are not in general rational multiples of $\pi$.


