Relation between the characters of subgroups of a finite group

Question

Let $ H $ and $ K $ be subgroups of a finite group $ G $. Let $ \chi_1(H) $ and $ \chi_1(K) $ denote the trivial characters of $ H $ and $ K $ over an algebraically closed field of characteristic $ 0 $. How "Mackey decomposition"would help us to prove that $ <\chi_1(H)^G, \chi_1(K)^G>_G $ equals the number of $ (H, K) $-bouble cosets