Given a set of $n$ angles: $\{A_0,A_1,.....,(n-2)\pi-\sum_0^{n-2}A_i\}$
How can we determine which ordering from this set can form a consistent linear equilateral shape ?
For instance $\{2\pi/3,\pi/4,\pi/4,5\pi/6\}$ how can we discriminate this set from this peculiar ordering if it has an ability to form a quadrilateral shape ?
I tried bruteforcing all permutations of sets but I'm sure there should be some system of constraints that tightens number of trials at a significant level.
What I have thought of, beginning from smallest values , constant checking if the actual angle doesn't early-close the polygon or generate an out-of-shape like this:
I constructed a geo-applet to simulate what i'm trying to do, for 4 angles the constraint is obvious, 2 per 2 angles should be equal, 5 angles and above I don't know it should be way tricky to grasp.