choose k numbers k1,k2...km such that sigma(cos((2*ki+1)*pi/n))==0&&sigma(sin((2*ki+1)*pi/n))==0

that is  sigma(cos((2*ki+1)*pi/n)+sin((2*ki+1)*pi/n)*i)==0
because cos(k*theta)+i*sin(k*theta)==(cos(theta)+i*sin(theta)^k

so it is sigma(cos(pi/n)+i*sin(pi/n))^(2*ki+1)==0

I think this problem must involved this...