Answer
$k\left(\frac{r_2^{4}-r_1^{4}\cos(\theta)}{r_1^{4}r_2^{4}}\right)= 0$
Work Step by Step
From the previous part:
$$ks\left(\frac{r_2^{4}-r_1^{4}\cos(\theta)}{r_1^{4}r_2^{4}\sin^{2}(\theta)}\right)=0$$
Multiply by $\frac{\sin^{2}(\theta)}{s}$:
$$\frac{\sin^{2}(\theta)}{s}\cdot ks\left(\frac{r_2^{4}-r_1^{4}\cos(\theta)}{r_1^{4}r_2^{4}\sin^{2}(\theta)}\right)=\frac{\sin^{2}(\theta)}{s}\cdot 0$$
$$k\left(\frac{r_2^{4}-r_1^{4}\cos(\theta)}{r_1^{4}r_2^{4}}\right)= 0$$
