sin^2 A
=(sinB cos C +cos B sin C)^2
=sin^2 Bcos^2 C +2sinBsinCcosBcosC +cos^2 Bsin^2 C
=(1-cos^2 B)cos^2 C +cos^2 B(1-cos^2 C) +2sinBsinCcosBcosC
=cos^2 C+ cos^2 B -2cos^2 B cos^2 C +2sinBsinCcosBcosC
=cos^2 C+ cos^2 B -2(cosBcosC-sinBsinC)cosBcosC
=cos^2 C+ cos^2 B -2cos(B+C)cosBcosC
=cos^2 C+ cos^2 B +2cos(180-B-C)cosBcosC
=cos^2 C+ cos^2 B +2cosAcosBcosC