Weird inequality problem.

Algebra Level 5

Determine the least real number $\xi$ such that the inequality

$\left|ab(a^2-b^2)+bc(b^2-c^2)+ca(c^2-a^2)\right|\leqslant \xi(a^2+b^2+c^2)^2$

holds for all real numbers $a,b$ and $c$ .