How do I show that $\displaystyle \pi$/9 is a root of 33*tan(x)^4-27*tan(x)^2-tan(x)^6+3?
Thank you, Catherine. Yes putting t=Pi/9 in
tan(3t) = (3tan(t)-tan(t)^3) / (1-3tan(t)^2)
looks like it will do it.
(for some reason your identity has
disappeared, but in case someone reads this I put it
back here so they would know what your reply was about).