electromagnetism - Explanation of $sin(theta) > 1$ for total internal reflection

Reading about total internal reflection, and I understand that it occurs when the sine of the refracted angle is greater than 1. What I don't see is how you ever have a $\sin \theta > 1$. Jackson says

This means that $\theta$ is a complex angle with a purely imaginary cosine...

how does this help explain it? What, for that matter, is the physical explanation for a complex angle?