Kα is emitted for transition from 2 → 1 = λ1 Energy released = E1
Kγ is emitted for transition from 4 → 1 = λ2 Energy released = E2
Lβ is emitted for transition from 4 → 2 = λ3 Energy released = E3
So E2 = E3 + E1
E3 = E2 - E1
we know that E = hc/λ ..
hc/λ3 = hc/λ2 - hc/λ1
1/λ3 = 1/λ2 - 1/λ1
1/λ3 = λ1 - λ2 / λ1λ2
so λ3 = λ1λ2 / λ1 - λ2