Parametric, Polar and Vector-Valued Functions · Superchallenge problem

A particle moves on the ellipse $\mathbf{r}(t)=\langle 3\cos t,\;2\sin t\rangle$. Let $\varphi$ be the angle between its position vector $\mathbf r$ and its velocity $\mathbf v$. Find the smallest value that $\sin\varphi$ takes.