More of an observation really.
WolframAlpha gives the result as exactly 33273.
tan^{6}(pi/9) is the root of x^333273x^2+11691x27 near x = 0.00232485 etc.
tan^{6}(2pi/9) is the root of x^333273x^2+11691x27 near x = 0.349045 etc.
tan^{6}(4pi/9) is the root of x^333273x^2+11691x27 near x = 33272.6 etc.
We can sum the roots of ax^3 + bx^2 + cx + d = 0 using this: http://mathforum.org/library/drmath/view/61024.html
giving b/a or 33273.
Edited on January 26, 2015, 10:00 pm

Posted by broll
on 20150126 21:42:55 