In the figure below, assume that the white hexagons are all identical and regular (they each have equal sides, equal angles) and that the colored figures are all congruent. Assuming that the distance from A to B is one unit, find the exact distance from A to C in terms of the angle theta shown.

Tristar

Make no other assumptions about the relative angles, keeping in mind that the picture changes when theta changes. (Click HERE for a crude animation demonstrating this.)