Show that every phase path encircles the origin infinitely

Question

A damped linear oscillator satisfies the equation

x^·· + x^· + x = 0.

Show that the polar equations for the motion of the phase points are

r^· = -r sin² θ,      θ^· = -(1 + (1/2)sin 2θ).

Show that every phase path encircles the origin infinitely many times in the clockwise direction. Show further that these phase paths terminate at the origin.