Does confinement imply CP invariance of the strong interactions?

The strong coupling constant $1\mathrm{/}{g}^2$ and the vacuum angle $\theta$ of the SU(3) Yang-Mills theory are investigated in the infrared limit under the renormalization group flow. It is shown that the theory has an infrared attractive fixed point at $1\mathrm{/}{g}^2=\theta =0$, which leads to linear confinement and naturally solves the strong CP problem. In particular, any initial value of $\theta \mathrm{\ne }0$ is found to be driven to $\theta =0$ at macroscopic distances, where quarks and gluons freeze into hadrons by the confinement mechanism.