As mentioned in an earlier problem (Problem 19, Section 3.3), a common incorrect proposal...

As mentioned in an earlier problem (Problem 19, Section 3.3), a common incorrect proposal often advanced by amateur mathematicians to solve the ancient problem of constructing the trisectors of an angle with the Euclidean tools is to lay out equal distances AD and AE on the sides of the angle to be trisected, then trisect the segment joining D and E, as shown. Prove that this never works, for any angle, that, in fact,

m∠LAM > m∠DAL = m∠MAE