Can you find the point of intersection?

Calculus Level 2

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

{x33xy2=a3yx2y3=b.\begin{cases} \begin{aligned} x^{3}-3xy^{2}&=a \\ 3yx^{2}-y^{3}&=b. \end{aligned} \end{cases}

Details and Assumptions:

  • aa and bb are real numbers.
  • The angle of intersection of curves is the angle between the tangents to the curves at the point of intersection.
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