In this paper we study discreteness of complex hyperbolic triangle groups of type
[
m
,
m
,
0
;
3
,
3
,
2
]
[m,m,0;3,3,2]
, i.e., groups of isometries of the complex hyperbolic plane generated by three complex reflections of orders
3
,
3
,
2
3,3,2
in complex geodesics with pairwise distances
m
,
m
,
0
m,m,0
. For fixed
m
m
, the parameter space of such groups is of real dimension one. We determine intervals in this parameter space that correspond to discrete and to non-discrete triangle groups.