We report measurements of the superconducting transition temperature, Tc, in CoO/Co/Cu/Co/Nb multilayers as a function of the angle α between the magnetic moments of the Co layers. Our measurements reveal that Tc(α) is a nonmonotonic function, with a minimum near α=π/2. Numerical self-consistent solutions of the Bogoliubov-de Gennes equations quantitatively and accurately describe the behavior of Tc as a function of α and layer thicknesses in these superconductor/spin-valve heterostructures. We show that experimental data and theoretical evidence agree in relating Tc(α) to enhanced penetration of the triplet component of the condensate into the Co/Cu/Co spin valve in the maximally noncollinear magnetic configuration. © 2014 American Physical Society.