  The problem of finding the zeros of the sum of two maximally monotone
operators is of fundamental importance in optimization and variational
analysis. In this paper, we systematically study Attouch-Th\'era duality for
this problem. We provide new results related to Passty's parallel sum, to
Eckstein and Svaiter's extended solution set, and to Combettes' fixed point
description of the set of primal solutions. Furthermore, paramonotonicity is
revealed to be a key property because it allows for the recovery of all primal
solutions given just one arbitrary dual solution. As an application, we
generalize the best approximation results by Bauschke, Combettes and Luke [J.
Approx. Theory 141 (2006), 63-69] from normal cone operators to paramonotone
operators. Our results are illustrated through numerous examples.
