The theory would be CP invariant if one could eliminate both sources of CP violation through such a field redefinition. But this cannot be done unless θ θ = − − θ θ ′ . This is because even under such field redefinitions, the combination θ θ ′ + θ θ → → ( θ θ ′ − − α α ) + ( θ θ + α α ) = θ θ ′ + θ θ remains unchanged. For example, the CP violation due to the mass term can be eliminated by picking α α = θ θ ′ , but then all the CP violation goes to the θ-term which is now proportional to θ θ ¯ ¯ . If instead the θ-term is eliminated through a chiral transformation, then there will be a CP violating complex mass with a phase θ θ ¯ ¯ . Practically, it is usually useful to put all the CP violation into the θ-term and thus only deal with real masses.