Can you find the point of intersection?

Calculus Level 2

Find the angle (in degrees) of intersection of the curves

$\begin{cases} \begin{aligned} x^{3}-3xy^{2}&=a \\ 3yx^{2}-y^{3}&=b. \end{aligned} \end{cases}$

Details and Assumptions:

$a$ and $b$ are real numbers.
The angle of intersection of curves is the angle between the tangents to the curves at the point of intersection.