Normal and branch restriction of a trigonometric curve

A curve is defined parametrically by \(x=3\tan t\) and \(y=2\sec t\), where \(-\frac{\pi}{2}<t<\frac{\pi}{2}\).

1. Using calculus, find the gradient of the normal to the curve at the point where \(t=\frac{\pi}{6}\).[3]
2. Eliminate \(t\) to obtain a Cartesian equation of the curve, stating any restriction on \(y\). Explain why the Cartesian equation alone includes points that do not belong to the parametric curve.[4]