(hereafter referred to as KZ) have shown that situations can arise where the property of entanglement of quantum systems is itself an entangled property. For that purpose they considered a three-particle system described by the Greenberger-Horne-Zeilinger (GHZ) state [@GHZ] $$|\Psi \rangle = \frac{1}{\sqrt{2}} (|z+ \rangle_1 |z+ \rangle_2 |z+ \rangle_3
+ |z- \rangle_1 |z- \rangle_2 |z- \rangle_3),$$ where $|z+ \rangle_i$ ($|z- \rangle_i$) represents a state of spin-up (-down) for particle $i$, $i=1,2,3$, along some quantization $z$ axis which in general will differ from one particle to the other. We can regard the three particles as flying apart from a common source, each of them subsequently entering its own Stern-Gerlach apparatus oriented along an arbitrary measurement direction $\vec{e}_i$ in three-dimensional space, this direction being specified by the polar and azimuthal angles $\vartheta_i$ and $\varphi_i$. It is assumed that at the time of measurement the particles 1, 2, and 3 may be arbitrarily far apart so that the acts of measurement by respective observers 1, 2, and 3 can be considered to have a spacelike separation. KZ first showed that the correlation function $E_{12}$ obtained by unconditionally averaging the products of the results of the measurements on particles 1 and 2 factorizes into 