  We consider Toeplitz determinants whose symbol has: (i) a one-cut regular
potential $V$, (ii) Fisher--Hartwig singularities, and (iii) a smooth function
in the background. The potential $V$ is associated with an equilibrium measure
that is assumed to be supported on the whole unit circle. For constant
potentials $V$, the equilibrium measure is the uniform measure on the unit
circle and our formulas reduce to well-known results for Toeplitz determinants
with Fisher--Hartwig singularities. For non-constant $V$, our results appear to
be new even in the case of no Fisher--Hartwig singularities. As applications of
our results, we derive various statistical properties of a determinantal point
process which generalizes the circular unitary ensemble.
