Originally Posted by
Jhevon just apply the addition formula for sine (and cosine) over and over
Recall: $\displaystyle \sin (\alpha + \beta ) = \sin \alpha \cos \beta + \sin \beta \cos \alpha$
and $\displaystyle \cos (\alpha + \beta ) = \cos \alpha \cos \beta - \sin \alpha \sin \beta$
Now, you have three terms in the sum for the angles. just apply the rules two at a time
example: $\displaystyle \sin (A + B + C) = \sin [(A + B) + C] = \sin (A + B) \cos C + \sin C \cos (A + B)$
and then you can apply the formulas i mentioned on $\displaystyle \sin (A + B)$ and $\displaystyle \cos (A + B)$