Lee. I finally got the chance to try your code, I'm still at awe how were you able to write the code with very few lines. [how did you manage that?]
I notice there are four pieces although connected to each other did not position itself correctly on the board. or is it just me.
Indeed, it is not a complete solution since I am only comparing the interior angles of
pairs of pieces, and not groups of 3, 4, 5,...,n pieces. The ambiguity in the position of the last four pieces arises because I am comparing the outer angles of the edge pieces (i.e. testing for summation to pi radians, rather than 2pi), and several positions will pass this test.