Question 327934
Here are the identities you need,
{{{ sin(x+y)=sin(x)cos(y)+cos(x)sin(y) }}}
{{{sin(x-y)=sin(x)cos(y)-cos(x)sin(y)}}}
{{{cos(x+y)=cos(x)cos(y)+sin(x)sin(y)}}}
{{{cos(x-y)=cos(x)cos(y)-sin(x)sin(y)}}}
{{{sin(2x)=2sin(x)cos(x)}}}
{{{cos(2x)=cos^2(x)-sin^2(x)}}}
I'll start you out with the first term.
{{{sin(B+2C)=sin(B)cos(2C)+cos(B)sin(2C)}}}
{{{sin(B+2C)=sin(B)(cos^2(C)-sin^2(C))+cos(B)(2sin(C)cos(C))}}}
{{{sin(B+2C)=sin(B)cos^2(C)-sin(B)sin^2(C)+2cos(B)2sin(C)cos(C)}}}
Continue in this fashion and then work backwards to get the right hand side. 
Watch the signs and the A,B, and C's. 
Good luck.