  We develop the theory of jitter radiation from GRB shocks containing
small-scale magnetic fields and propagating at an angle with respect to the
line of sight. We demonstrate that the spectra vary considerably: the
low-energy photon index, $\alpha$, ranges from 0 to -1 as the apparent viewing
angle goes from 0 to $\pi/2$. Thus, we interpret the hard-to-soft evolution and
the correlation of $\alpha$ with the photon flux observed in GRBs as a combined
effect of temporal variation of the viewing angle and relativistic aberration
of an individual thin, instantaneously illuminated shell. The model predicts
that about a quarter of time-resolved spectra should have hard spectra,
violating the synchrotron $\alpha=-2/3$ line of death. The model also naturally
explains why the peak of the distribution of $\alpha$ is at $\alpha\approx-1$.
The presence of a low-energy break in the jitter spectrum at oblique angles
also explains the appearance of a soft X-ray component in some GRBs and a
relatively small number of them. We emphasize that our theory is based solely
on the first principles and contains no {\it ad hoc} (phenomenological)
assumptions.
