N[(∫_0^((2 π)/a))(∫_0^((2 π)/a))(∫_0^((2 π)/a))((Coth[((6 J S (Sqrt[1-(1/9) (((Cos[a x]+Cos[a y]+Cos[a z]))^2)]))/T)])/(Sqrt[1-(1/9) (((Cos[a x]+Cos[a y]+Cos[a z]))^2)]))\[DifferentialD]x\[DifferentialD]y\[DifferentialD]z,Assumptions->{a>0&&a∈Reals},Assumptions->{S>0&&S∈Reals},Assumptions->{J>0&&J∈Reals}]