The equation of a curve is \(x^3 y - 3xy^3 = 2a^4\), where \(a\) is a non-zero constant.

(i) Show that \(\frac{dy}{dx} = \frac{3x^2 y - 3y^3}{9xy^2 - x^3}\).

(ii) Hence show that there are only two points on the curve at which the tangent is parallel to the \(x\)-axis and find the coordinates of these points.