  We analytically prove the necessary and sufficient criterion for the full
separability of three-qubit Greenberger-Horne-Zeilinger (GHZ) diagonal states.
The corresponding entanglement is exactly calculable for some GHZ diagonal
states and is tractable for the others using the relative entropy of
entanglement. We show that the biseparable criterion and the genuine
entanglement are determined only by the biggest GHZ diagonal element regardless
of all the other smaller diagonal elements. We have completely solved the
entanglement problems of three-qubit GHZ diagonal states.
