  Intrinsic galaxy alignments yield an important contribution to the observed
statistics of galaxy shapes. The general bias expansion for galaxy sizes and
shapes in three dimensions has been recently described by Vlah, Chisari \&
Schmidt using the general perturbative effective field theory (EFT) framework,
in analogy to the clustering of galaxies. In this work, we present a formalism
that uses the properties of spherical tensors to project galaxy shapes onto the
observed sky in the flat-sky approximation and compute the two-point functions
at next-to-leading order as well as the leading-order three-point functions of
galaxy shapes and number counts. The resulting expressions are given in forms
that are convenient for efficient numerical implementation. For a source
redshift distribution typical of Stage IV surveys, we find that that nonlinear
intrinsic alignment contributions to galaxy shape correlations become relevant
at angular wavenumbers $l \gtrsim 100$.
