The recently fabricated two-dimensional magnetic materials Cu9X2 cpa 6 ·xH2O cpa=2-carboxypentonic acid and X=F,Cl,Br have copper sites which form a triangular kagome lattice TKL , formed by introducing small triangles “a-trimers” inside of each kagome triangle “b-trimer” . We show that in the limit where spins residing on b-trimers have Ising character, quantum fluctuations of XXZ spins residi...