  We study the breakdown of the magnetization plateau at the magnetization
M=M_{S}/3 (M_{S} is the saturation magnetization) of the S=1/2 anisotropic spin
chain with ferromagnetic-ferromagnetic-antiferromagnetic interactions. We
consider the model with the isotropic ferromagnetic (trimer) coupling J_{F},
and anisotropic antiferromagnetic coupling (J_{x}=J_{y}=J_{AF} and J_{z}=\Delta
J_{AF}). For the limit of large \gamma\equiv J_{F}/J_{AF}, the model is
equivalent to the S=3/2 XXZ chain with the exchange anisotropy \Delta. There is
a phase transition between the plateau (small-\gamma) and the no-plateau
(large-\gamma) regions. This phase transition is of the
Berezinskii-Kosterlitz-Thouless type, and we determine the phase boundary from
the numerical diagonalization data. For \Delta=1, in particular, the phase
transition between the plateau and the no-plateau regions occurs at the point
\gamma_{c}=15.4.
