How to eliminate $\theta$? While doing a sum I was stuck in a particular step:
$$r_1= \frac{4a \cos \theta }{\sin^2 \theta}$$ and $$r_2=\frac{4a \sin \theta }{\cos^2 \theta}$$
How to eliminate $\theta$ ?

$$\frac{r_2}{r_1}=\tan^3(\theta) \iff \theta = \arctan(\sqrt[3]{\frac{r_2}{r_1}}) \pmod \pi$$
Edit: I've posted another answer which might better fit what you're looking for
