The curve \(C\) has the equation \(x^3+y^3 = 3xy\).
Show that there is no point of inflection on \(C\). You may assume that
the origin is not a point of inflection.
The part of \(C\) which lies in the first quadrant is a closed loop
touching the axes at the origin. By converting to polar coordinates,
or otherwise, evaluate the area of this loop.