  We generalize our discussions and give more general physical applications of
a new solution to the strong CP problem with magnetic monopoles as originally
proposed by the author$^1$. Especially, we will discuss about the global
topological structure in the relevant gauge orbit spaces to be clarified. As it
is shown that in non-abelian gauge theories with a $\theta$ term, the induced
gauge orbit space with gauge potentials and gauge functions restricted on the
space boundary $S^2$ has a magnetic monopole structure and the gauge orbit
space has a vortex structure if there is a magnetic monopole in the ordinary
space. The Dirac's quantization conditions in the quantum theories ensure that
the vacuum angle $\theta$ in the gauge theories must be quantized. The
quantization rule is given by $\theta=2\pi/n~(n\neq 0)$ with n being the
topological charge of the magnetic monopole. Therefore, the strong CP problem
is automatically solved in the presence of a magnetic monopole of charge $\pm
1$ with $\theta=\pm 2\pi$, or magnetic monopoles of very large total
topological charge ($|n|\geq 10^92\pi$) if it is consistent with the abundance
of magnetic monopoles. Where in the first case with a magnetic monopole of
topological charge 1 or -1, we mean the strong CP-violation can be only very
small by the measurements implemented so far. Since $\theta=\pm 2\pi$
correspond to different monopole sectors, the CP can not be conserved exactly
in strong interactions in this case. In the second case, the strong CP cannot
be conserved either for large but finite n. The fact that the strong
CP-violation measured so far can be only so small or vanishing may be a signal
for the existence of magnetic monopoles. We also conjecture that the parity
violation and CP violation in weak interaction fundamentally may intimately
