  In three-band BCS superconductors with repulsive interband interactions,
frustration between the bands can lead to an inherently complex gap function,
arising out of a phase difference between the bands in the range 0 and {\pi}.
Since the complex conjugate of this state is also a solution, the ground state
is degenerate, and there appears a time-reversal-symmetry-broken state. In this
paper we investigate the existence of this state as a function of interband
coupling strength and show how a new phase transition appears between the TRSB
and conventional BCS states.
