  One of the major theoretical riddles in shear banding instabilities is the
angle that the shear band chooses spontaneously with respect to the principal
stress axis. Here we employ our recent atomistic theory to compute analytically
the angle in terms of the characteristics of the Eshelby inclusion that models
faithfully the eigenfunction of the Hessian matrix that goes soft at the
plastic instability. We show that loading protocols that do not conserve volume
result in shear bands at angles different from 45$^o$ to the strain axis; only
when the external strains preserve volume like in pure shear, the shear bands
align precisely at 45$^o$ to the strain axis. We compute an analytic formula
for the angle of the shear band in terms of the characteristics of the loading
protocol; quantitative agreement with computer simulations is demonstrated.
