How can I count the number of concave interior angles in a polygon?

I would like some advice on setting up a workbench that could retrieve the number of interior angles in a polygon that are classed as concave (i.e. >180 degrees).

So far I have the following:

1. run my polygon featureclass through the 'convexity filter' to obtain only concave polygons.
2. I then use the 'Orientor' to assign the right hand rule before passing it through the 'VertexAngleCalculator'.
3. I then use a tester to filter those angle that are negative (i.e. concave).
4. Use 'statistics calculator grouped by original polygon UID to get the total count of features.
5. merge these attributes with the original feature class.

This works fine as long as the first/last vertex in the polygon is not a concave angle. This is because the 'VertexAngleCalculator' returns a value of '0' for the start/end vertex - and therefore cannot be classified.

Unless there is a simpler way to obtain all interior angles for each polygon, my thoughts would be to re-run the process a second time, first shifting the order of vertices by 1 index place. Then removing all features from both passes with a angle attribute of 0, and removing duplicates from the first pass that have the same geometry and angle attribute as in the second pass. Unfortunately I have no idea how to do this in FME.

Any help would be greatly appreciated!