Conservation of angular moment and crossing of orbits

The earth moves in a circular orbit with radius $R$ around the sun with speed $V$ . A comet also orbits the sun in a path such that the perihelion is at $\frac{R}{2}$ at a speed $2V$ . The question is to deduce from the conversation of angular momentum that the angle at which their orbits cross is $\frac{\pi}{4}$ .

Now, I know that angular momentum is $r^{2}\dot{\theta}m$ but I am unsure how to apply this to the question and I am unsure what $\dot{\theta}$ is representing here. And do I also have to consider the momentum of the earth?