MathNet 2013 Câu hỏi 82

Cho $a,b,c,d\gt 0$ thỏa $abcd=1$. Chứng minh
$$\frac1{a+b+2}+\frac1{b+c+2}+\frac1{c+d+2}+\frac1{d+a+2}\le1.$$