  In [9], Terao proved the freeness of multi-Coxeter arrangements with constant
multiplicities by giving an explicit construction of bases. Combining it with
algebro-geometric method, Yoshinaga proved the freeness of the extended Catalan
and Shi arrangements in [11]. However, there have been no explicit
constructions of the bases for the logarithmic derivation modules of the
extended Catalan and Shi arrangements. In this paper, we give the first
explicit construction of them when the root system is of the type $A_2$.
