  We provide a complete analysis of mixed three-qubit states composed of a GHZ
state and a W state orthogonal to the former. We present optimal decompositions
and convex roofs for the three-tangle. Further, we provide an analytical method
to decide whether or not an arbitrary rank-2 state of three qubits has
vanishing three-tangle. These results highlight intriguing differences compared
to the properties of two-qubit mixed states, and may serve as a quantitative
reference for future studies of entanglement in multipartite mixed states. By
studying the Coffman-Kundu-Wootters inequality we find that, while the amounts
of inequivalent entanglement types strictly add up for pure states, this
``monogamy'' can be lifted for mixed states by virtue of vanishing tangle
measures.
