Perhaps the reason that so few mathematicians "have grasped that sine 75 degrees raised to the power of 10 equals sine 45 degrees" is that sin(75 degrees) = (1 + sqrt(3))^10/32768, while sin(45 degrees) = sqrt(2)/2, which are different numbers (although they happen to agree to 3 decimal places).
Perhaps the reason that so few mathematicians "have grasped that sine 75 degrees raised to the power of 10 equals sine 45 degrees" is that sin(75 degrees) = (1 + sqrt(3))^10/32768, while sin(45 degrees) = sqrt(2)/2, which are different numbers (although they happen to agree to 3 decimal places).