Notice that equation has five roots, whose sum equals (from Vieta's theorem). It also means that their real parts also sum up to zero, i.e.
By trig identities we have (the same result can be obtained by symmetry of the picture), so .
has five roots, whose sum equals 
(from Vieta's theorem). It also means that their real parts also sum up to zero, i.e. 
(the same result can be obtained by symmetry of the picture), so 
.
