Conic Sections and Parametric Equations · Superchallenge problem

For $0<t<\dfrac{\pi}{2}$, draw the four lines tangent to the ellipse $\dfrac{x^2}{9}+\dfrac{y^2}{4}=1$ at the points $(\pm3\cos t,\ \pm2\sin t)$ (all four sign choices). They bound a rhombus. Find the smallest possible area of this rhombus.