The anisotropic field dependence of the Sommerfeld coefficient gamma has been measured down to B-->0 by combining specific heat and Hall probe magnetization measurements in MgB2 single crystals. We find that gamma(B,theta) is the sum of two contributions arising from the sigma and pi band, respectively. We show that gammasigma(B,theta)=B/Bc2(theta) where Bc2(theta)=Bc2ab/sqrt[sin2theta+Gamma2cos2theta] with Gamma approximately 5.4 (theta being the angle between the applied field and the c axis) and gammapi(B,theta)=gammapi(B)=B/Bpi(B). The "critical field" of the pi band Bpi is fully isotropic but field dependent increasing from approximately 0.25 T for B< or =0.1 T up to 3 T approximately Bc2c for B-->3 T. Because of the coupling of the two bands, superconductivity survives in the pi band up to 3 T but is totally destroyed above for any orientation of the field.