[john.gersh]

The alignment needn't be difficult.

Make sure Smart Alignment Guides is enabled.
Using the filled-sector tool, make a circular segment. (Holding shift while drawing ensures it's circular.)
Drag one corner handle to 0 degrees and the other to 15.
Duplicate the segment. Rotate the new segment by 15 degrees. (Geometry Inspector thumbwheel edit field). Snap the new segment to the original. The smart guides do the snapping and indicate when you're aligned in both dimensions.
Repeat till done.

Tedious, but not difficult. You can speed it up by grouping a few segments and then duplicating and aligning the groups.