A curve has polar equation \(r=\dfrac{1}{1-\cos\theta}\), for \(0\lt\theta\lt 2\pi\). Find, in the form \(y^2=f(x)\), the cartesian equation of the curve.

Hence sketch the curve, and shade the region whose area is given by \(\dfrac12\int_{\pi/2}^{3\pi/2}\dfrac{1}{(1-\cos\theta)^2}\,d\theta\).

Using the cartesian equation of the curve, find the area of this region.