Conservation of angular moment and crossing of orbits

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

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