### Simplification of atan

I'm teaching a course on dynamical systems based on the book by Devaney. Today I tried to show the map $f(\theta)=2\theta$ on the circle using Sage, where $\theta$ is given in radians. I could not find functions already defined to perform addition in $\mathbb{R}$ modulo $2\pi$, so I tried to devise my own. I stumbled upon this problem:

atan(sin(1/5*pi)/cos(1/5*pi))

produces

arctan(4*sin(1/5*pi)/(sqrt(5) + 1)).

Is there a way to obtain 1/5*pi?

(By the way, _.simplify() does nothing in this case.)