In 2010, Murty and Thangadurai [MuTh10] provided a criterion for the set equidistribution of residue classes of subgroups in (Z/nZ) *. In this article, using similar methods, we study set equidistribution for some class of subsets of (Z/nZ) *. In particular, we study the set equidistribution modulo 1 of cosets, complement of subgroups of the cyclic group (Z/nZ) * and the subset of elements of fixed order, whenever the size of the subset is sufficiently large.