We divide any angle by this method into the ratio of x:y:x but not x:x:x so the trisection method you proposed is actually a method for partitioning an angle into ratio x:y:x (where values of x and y can be calculated for general case. You can try it and show that x is not equal to y !!!). Talking generally, we can divide any arbitrary angle into a paliandromic ratio by this chord sectioned method.(i.e. for 5 parts, angle wil be divided into ratio a:b:c:b:a , etc). There are different auxilliary curves like hyperbola(for trisection only), spiral(for n section), sinusoidal wave(for n section), etc which can trisect or nsect any given angle. Sometimes only intuition can give wrong results bro so read more and derive more.

We divide any angle by this method into the ratio of x:y:x but not x:x:x so the trisection method you proposed is actually a method for partitioning an angle into ratio x:y:x (where values of x and y can be calculated for general case. You can try it and show that x is not equal to y !!!). Talking generally, we can divide any arbitrary angle into a paliandromic ratio by this chord sectioned method.(i.e. for 5 parts, angle wil be divided into ratio a:b:c:b:a , etc). There are different auxilliary curves like hyperbola(for trisection only), spiral(for n section), sinusoidal wave(for n section), etc which can trisect or nsect any given angle. Sometimes only intuition can give wrong results bro so read more and derive more.