[newbie] trying to simplify goniometric expression

I defined the following function:
phicalp(m,omega):=-sum(atan(omega/(4*(cos((k*%PI)/(2*m+1)))^2)),k,1,m);

I expected that the following "test-expression" should give me "-omega" as 
a result:
ratsimp(tan(phicalp(1,omega))),trigexpand=super;

however maxima doesn't seem to simplify the denominator to one:
                                       omega
(%o2)                            - -----------
                                         2 %PI
                                    4 cos (---)
                                            3

Which is the correct approach for this kind of simplification?

thanks in advance
hugo
p.s. accept my apologies if this message is posted twice. Since my email 
address was changed recently, the message was initially refused, so I had 
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