Find a tangent, normal and exact triangle area

A curve has $x=3\cos\theta$, $y=2+\sin\theta$, $0\le\theta\le2\pi$.

(a) Show that the tangent at $P$, where $\theta=\pi/6$, is $y+(\sqrt3/3)x-4=0$.

(b) Find the normal at $P$.

(c) The tangent and normal meet the y-axis at $T$ and $N$ respectively. Find the exact area of triangle $PNT$.