  A system of three coupled quantum dots in a triangular geometry (TQD) with
electron-electron interaction and symmetrically coupled to two leads is
analyzed with respect to the electron transport by means of the numerical
renormalization group. Varying gate potentials this system exhibits extremely
rich range of regimes with different many-electron states with various local
spin orderings. It is demonstrated how the Luttinger phase changes in a
controlled manner which then via the Friedel sum rule formula exactly
reproduces the conductance through the TQD system. The analysis of the
uncoupled TQD molecule from the leads gives a reliable qualitative
understanding of various relevant regimes and gives an insight into the phase
diagram with the regular Fermi liquid and singular-Fermi liquid phases.
