  We give a complete solution for the three-tangle of mixed three-qubit states
composed of a generalized GHZ state, a|000>+b|111>, and a generalized W state,
c|001>+d|010>+f|100>. Using the methods introduced by Lohmayer et al. we
provide explicit expressions for the mixed-state three-tangle and the
corresponding optimal decompositions for this more general case. Moreover, as a
special case we obtain a general solution for a family of states consisting of
a generalized GHZ state and an orthogonal product state.
