Breifly, I ran across Marks construction on Jim Loy's webpage about trisection and it led here. I've been goofing around with trisections for a year or so.
I am at a Homer Simpson level of math, so don't know how to properly figure out how accurate a construction is. I have been relying on C.a.R., the software I use, to judge.
The problem is that with the last few versions of TRiSeK, it does not come up with consistent numbers. Points placed on differnt places on the same lines will come up with very different numbers. Even when I anchor the points on a circle, the reading from one side is not the same as from the other side of the vertex. They will often be on either side of perfect.
Interestingly, C.a.R. has no trouble measuring Mark's amazing trisector, so it doesn't appear to be the number of decimal places.