Unramified degree three invariants of reductive groups

We prove that if G is a reductive group over an algebraically closed field F  , then for a prime integer p≠char(F)p≠char(F), the group of unramified Galois cohomology Hnr3(F(BG),Qp/Zp(2)) is trivial for the classifying space BG of G if p is odd or the commutator subgroup of G is simple.