Find sin(α+β+γ)\sin(\alpha + \beta + \gamma)sin(α+β+γ) in terms of sines and cosines of single angles.
cos(α+β+γ)\cos(\alpha + \beta + \gamma)cos(α+β+γ)
sinαcosβcosγ+cosαsinβcosγ+cosαcosβsinγ−sinαsinβsinγ\sin\alpha\cos\beta\cos\gamma + \cos\alpha\sin\beta\cos\gamma + \cos\alpha\cos\beta\sin\gamma - \sin\alpha\sin\beta\sin\gammasinαcosβcosγ+cosαsinβcosγ+cosαcosβsinγ−sinαsinβsinγ
sinα+sinβ+sinγ−sinαsinβsinγ\sin\alpha + \sin\beta + \sin\gamma - \sin\alpha\sin\beta\sin\gammasinα+sinβ+sinγ−sinαsinβsinγ
sinαsinβsinγ+sinαcosβcosγ+cosαsinβcosγ+cosαcosβsinγ\sin\alpha\sin\beta\sin\gamma + \sin\alpha\cos\beta\cos\gamma + \cos\alpha\sin\beta\cos\gamma + \cos\alpha\cos\beta\sin\gammasinαsinβsinγ+sinαcosβcosγ+cosαsinβcosγ+cosαcosβsinγ