  We determine the phase diagram and chiral condensate for lattice QCD with two
flavors of twisted-mass fermions in the presence of nondegenerate up and down
quarks, discretization errors and a nonzero value of $\Theta_{\rm QCD}$.
Although such a theory has a complex action and cannot, at present, be
simulated, the results are needed to understand how to tune to maximal twist in
the presence of electromagnetism, a topic discussed in a companion paper. We
find that, in general, the only phase structure is a first-order transition of
finite length. Pion masses are nonvanishing throughout the phase plane except
at the endpoints of the first-order line. Only for extremal values of the twist
angle and $\Theta_{\rm QCD}$ ($\omega=0$ or $\pi/2$ and $\Theta_{\rm QCD}=0$ or
$\pi$) are there second-order transitions.
