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In regards to people tackling a proof trisecting an angle, a case can be made that it isn’t always a worthless endeavor. In my case I am looking at it as a way to keep my mind and thinking active.
The easiest thing to do is to prove that it is impossible to trisect any angle precisely. However there is still the question of is there any method to effectively trisect any angle to an acceptable accuracy in a limited number of steps using only a compass and unmarked straight edge. This is a different issue and is a valid question.