Write $x=\cos \alpha, y=\sin \alpha$. Then the equation simplifies to $\cos 3\alpha=\frac{3}{5}$ and hence $\sin 3\alpha=\pm \frac{4}{5}$ and hence $|20y^3-15y|=4$.

Write $x=\cos \alpha, y=\sin \alpha$. Then the equation simplifies to $\cos 3\alpha=\frac{3}{5}$ and hence $\sin 3\alpha=\pm \frac{4}{5}$ and hence $|20y^3-15y|=\pm 4$.