N[\int^{\frac{2\pi}{a}}_{0}\int^{\frac{2\pi}{a}}_{0}\int^{\frac{2\pi}{a}}_{0}\frac{Coth[\frac{6SJ\sqrt{1-\frac{(Cos[x a]+Cos[y a]+Cos[z a])^2}{9}}}{2T}]}{\sqrt{1-\frac{(Cos[x a]+Cos[y a]+Cos[z a])^2}{9}}}dxdydz]