  Bowman and Bradley proved an explicit formula for the sum of multiple zeta
values whose indices are the sequence (3,1,3,1,...,3,1) with a number of 2's
inserted. Kondo, Saito and Tanaka considered the similar sum of multiple
zeta-star values and showed that this value is a rational multiple of a power
of \pi. In this paper, we give an explicit formula for the rational part. In
addition, we interpret the result as an identity in the harmonic algebra.
