  Introducing a vacuum angle $\theta_h$ in a strongly interacting hidden sector
like QCD, we study how $\theta_h$ affects physical quantities in a scale
invariant extension of the standard model with that hidden sector. In this
model the dynamical chiral symmetry breaking occurs in the hidden sector and
generates a scale $ \vert \langle {\bar q} q \rangle \vert $ which triggers
electroweak symmetry breaking. We find that the expression for a vacuum
expectation value of the Higgs field depends on $\theta_h$, while the condition
which determines the Higgs particle mass does not. This model contains the
hidden-sector pions $\pi^0$ and $\pi^{\pm}$ which are candidates for cold dark
matter, and we find the mass difference between the hidden-sector $\pi^0$ and
$\pi^{\pm}$ will not be negligible for $\theta_h \approx \pi$.
