Suppose $\theta \neq \frac pq * \pi$. Show ${\{e^{in\theta} : n \ \epsilon \ N}\}$ is dense in $S^1=\{x + iy: x^2 + y^2 = 1\} \subseteq C$
Prove that the orbit of an iterated rotation of 0 (by (A)(Pi), A irrational) around a circle centered at the origin is dense in the circle.