The Rost invariant has zero kernel for quasi-split trialitarian groups

The Book of Involutions includes the NON-trivial parts of a proof that the kernel of the Rost invariant is zero for quasi-split trialitarian groups. We record the missing (mechanical) details here. This note is recorded here on the arxiv only for the convenience of readers who like the style of The Book and obviously does not merit publication. A proof in Harder's style can be found in a paper by Chernousov (see the bibliography).