Cyclic

Algebra Level 4

Positive real $a$ , $b$ , $c$ , and $d$ are such that $a + b + c + d = 1$ , find the minimum of:

$\frac{a^3}{b + c} + \frac{b^3}{c + d} + \frac{c^3}{d + a} + \frac{d^3}{a + b} .$

This is part of the set My Problems and THRILLER