  We address the problem of counting walks by winding angle on the Kreweras
lattice, an oriented version of the triangular lattice. Our method uses a new
decomposition of the lattice, which allows us to write functional equations
characterising a generating function of walks counted by length, endpoint and
winding angle. We then solve these functional equations in terms of Jacobi
theta functions. By using this result in conjunction with the reflection
principle, we count walks confined to a cone of opening angle any multiple of
$\frac{\pi}{3}$, allowing us to extract asymptotic and algebraic information
for these walks. Our method and results extend analogously to three other
lattices, including the square lattice and triangular lattice. On the square
lattice, most of our results were derived by Timothy Budd in 2017, so the
current work can be seen as an extension of Budd's results to the three other
lattices that we consider. Budd's method of deducing these results was very
different, as it was based on an explicit eigenvalue decomposition of certain
matrices counting paths in the lattice.
