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

1. Show that \(\frac{dy}{dx} = \frac{2x^2 - y^2}{y^2 + 2xy}\).
2. Find the coordinates of the two points on the curve at which the tangent is parallel to the y-axis.