DE-MO 2021 Problem 5

a) Determine the largest real number $A$ with the following property: For all non-negative real numbers $x,y,z$ , one has $$\frac{1+yz}{1+x^2}+\frac{1+zx}{1+y^2}+\frac{1+xy}{1+z^2} \ge A.$$ b) For this real number $A$ , find all triples $(x,y,z)$ of non-negative real numbers for which equality holds in the above inequality.