  Spin liquids occuring in 2D frustrated spin systems were initially assumed to
appear at strongest frustration, but evidence grows that they more likely
intervene at transitions between two different types of order. To identify if
this is more general, we here analyze a generalization of the spatially
anisotropic triangular lattice (SATL) with antiferromagnetic XY interactions,
the spatially \emph{completely} anisotropic triangular lattice (SCATL). This
model can be implemented in experiments with trapped ions, ultra-small
Josephson junctions, or ultracold atoms in optical lattices. Using Takahashi's
modified spin-wave theory, we find indications that indeed two different kinds
of order are always separated by phases without magnetic long-range order. Our
results further suggest that two gapped, magnetically-disordered phases,
identified as distinct in the SATL, are actually continuously connected via the
additional anisotropy of the SCATL. As these results indicate, this additional
anisotropy -- allowing to approach quantum-disordered phases from different
angles -- can give fundamental insight into the nature of quantum disordered
phases. We complement our results by exact diagonalizations, which also
indicate that in part of the gapped non-magnetic phase, chiral long-range
correlations could survive.
