MathNet 2017-part-05 — 176 problems (EN–VI) Question 39

Let $a, b, c, d \in [0, 1]$. Prove that
$$
\frac{a}{1+b} + \frac{b}{1+c} + \frac{c}{1+d} + \frac{d}{1+a} + abcd \le 3.
$$