Find the point(s) on the ellipse $x = 3 \cos t$, $y = \sin t$, $0 \le t \le 2\pi$, closest to the point $\begin{pmatrix} -\frac{4\sqrt{3}}{3} \\ 0 \end{pmatrix}$.
(Hint: Minimize the square of the distance as a function of t.)
The point(s) on the ellipse closest to the given point is(are) $(-3, 0)$.
(Type ordered pairs. Use a comma to separate answers as needed.)
