Given an angle $\theta$ (in radians), write $\theta = 2\pi t + \phi$, where $\phi$ is between $0$ and $2\pi$, $0\leq \phi\lt 2\pi$, and $t$ is an integer. Call $k=2\pi t$ the number of "full circles" or "full turns" corresponding to the angle.
If $\theta = \frac{13\pi}{4}$, am I right that k=$2\pi$?