HINT: First use the given together with Lagrange's Theorem (in particular equation (4.8)) and Theorem 6.1.1 to show that . Next decompose into double cosets with respect to and and use equation (8.6). Now the identity belongs to some double coset, so we may assume that , in the line before equation (8.6). Finally this implies that in (8.6) , but all the other . (Why?) Use the resulting relation to get the desired result.