  A non-perturbative solution to strong CP problem is proposed. It is shown
that the gauge orbit space with gauge potentials and gauge tranformations
restricted on the space boundary in non-abelian gauge theories with a $\theta$
term has a magnetic monopole structure if there is a magnetic monopole in the
ordinary space. The Dirac's quantization condition in the corresponding quantum
theories ensures that the vacuum angle $\theta$ in the gauge theories must be
quantized. The quantization rule is derived as $\theta=2\pi/n~(n\neq 0)$ with n
being the topological charge of the magnetic monopole. Therefore, we conclude
that the strong CP problem is automatically solved non-perturbatively with the
existence of a magnetic monopole of charge $\pm 1$ with $\theta=\pm 2\pi$. This
is also true when the total magnetic charge of monopoles are very large
($|n|\geq 10^92\pi$) if it is consistent with the abundance of magnetic
monopoles. This implies that the fact that the strong CP violation can be only
so small or vanishing may be a signal for the existence of magnetic monopoles.
