Let θ be the angle of incidence at face AB, then for total internal reflection at face AB.
sinθ>C1=μ1μ2=√22
⇒sinθ>1√2 or sinθ>sin45o⇒θ>45o
For total internal reflection at face CD,
sinθ>sinC2=μ3μ2=√32⇒sinθ>√32
or sinθ>sin60 or θ>60o
Therefore, for total internal reflection at both the surfaces,
θmin=60o.