(sin theta+2sin3 theta+sin5 theta)/(sin3 theta+2sin5 theta+sin7 theta)=(sin3 theta)/(sin5 theta)

Solve sin7 theta=sin3 theta+sin theta

Prove that : (sin theta + 2 sin 3theta + sin 5theta)/(sin 3theta + 2 sin 5theta + sin 7theta) = (sin 3theta)/(sin 5theta)

sin theta + sin3 theta + sin5 theta = 0

4 sin 5 theta cos 3 theta sin 2 theta

(sin5 theta-2sin3 theta + sin theta) / (cos5 theta-cos theta) = tan theta

(sin7 theta+6sin5 theta+17sin3 theta+12sin theta)/(sin6 theta+5sin4 theta+12sin2 theta)

(sin7 theta+6sin5 theta+17sin3 theta+12sin theta)/(sin6 theta+5sin4 theta+12sin2 theta)=

(sin7 theta+6sin5 theta+17sin3 theta+12sin theta)/(sin6 theta+5sin4 theta+12sin2 theta)=

(sin theta+sin3 theta+sin5 theta)/(cos theta+cos3 theta+cos5 theta)=tan3 theta

The value of expression (sin theta+3sin3 theta+5sin5 theta+3sin7 theta)/(sin2 theta+2sin4 theta+3sin6 theta) where theta=(4 pi)/(5) is equal to