Let $C$ be the cardioid given by the polar equation $r = 1 − \cos(\theta)$ , $−\pi \le \theta \le \pi$.
(a) Find the intersection points of the curve with the line $\theta = \pi/4$.
(b) Find the intersection points of the curve with the circle $r = 1/2$.
(c) Find the slope of the tangent line to the curve at the point $(3/2,−2\pi/3)$.
(d) Find the length of the part of the curve in the fourth quadrant.