  Francis Brown used a certain evaluation formula for multiple zeta values
proved by Zagier to prove the injectivity of the homomorphism from the Motivic
Galois group to the automorphism of fundamental group of projective line
deleted three points. In this paper, we prove that any associators satisfies
this relation. As a consequence, this relation holds for motivic multiple zeta
values which is also proved in Brown's paper. We used certain cohomology theory
and Li's method for the computation.
