Late news (February 1993)
An incident that occurred several years ago , led to a brainwave that inspired an interesting method of solving the trisection problem.
I was waiting for a bus at Irtupaliyam ( a village that is situated about 3 Kilometers from Karunya Institute of Technology,Coimbatore)
when none less than a tree-twig provided food for thought!
After listlessly playing with the twig and inscribing patterns on the sand , the twig snapped in my hand and the three sections of twig
became the seed of a possible solution to the trisection problem.
A few weeks later i did integrate the idea into an iterative geometry construction and i was able to share this discovery with a few.
Though it is one more attempt of a trisection solution(?), it led to a theorem that i mention below.

Theorem of symmetric rotations : For any given straight
line divided into three equal line segments, the
perpendicular bisector of the middle segment is the
locus of all points at which the other two lines
subtend equal angles, as they rotate symmetrically
about the end points of the middle segment.

Corollary of the theorem : For any given
angle ,there must exist three equal and joined straight
lines such that the bisector of the angle is the
perpendicular bisector of one of the lines while the
other two lines subtend equal angles at the vertex of
the given angle and their ends lie on either arm of the
angle.
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Trisection Analytical engine
future