#4751 sin(12/11*%pi) should simplify to -sin(%pi/11)

[Stavros Macrakis]

Maxima reduces sin(a+%pi) to -sin(a) (with %piargs=true, the default).
It also expands sin(m/n*%pi) to an algebraic form for n in {2,3,4,6} (and ntrig adds {5,10}.

However, it does not currently reduce sin(m/n*%pi) when m/n > 1/2 and n not in {2,3,4,5,6,10}. Why doesn't it perform sin(11/7*%pi) => sin(-3/7*%pi), sin(71*%pi/7) => sin(%pi/7), sin(4*%pi/7) => sin(3*%pi/7), etc.?

Is there a package to do this?

Tested in Maxima 5.49.0 SBCL 2.5.1