`(sin7theta+6sin5theta+17sin3theta+12sintheta)/(sin6theta+5sin4theta+12sin2theta)` is equal to

(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)=

sintheta+sin7theta=sin4theta

sin2theta-sin4theta+sin6theta=0

sin2theta+sin4theta=sin6theta

sintheta+sin2theta+sin4theta+sin5theta=0

Sum to terms of the series sintheta sin2theta + sin2thetasin3theta + sin3theta sin4theta +..... is equal to

(sin3theta+sin5theta+sin7theta+sin9theta)/(cos3theta+cos5theta+cos7theta+cos9theta) is equal