Answer
$\cos(\theta)=\frac{r_2^{4}}{r_1^{4}}$
Work Step by Step
From the previous part if follows:
$$k\left(\frac{r_2^{4}-r_1^{4}\cos(\theta)}{r_1^{4}r_2^{4}}\right)= 0$$
$$r_2^{4}-r_1^{4}\cos(\theta)=0$$
$$r_1^{4}\cos(\theta)=r_2^{4}$$
$$\cos(\theta)=\frac{r_2^{4}}{r_1^{4}}$$
