Hardest Identity Evar involving sum and differences

[amd123]

Homework Statement

sin (x) + sin (3x) + sin (5x) + sin (7x) = 4cos(x)cos(2x)sin(4x)

Homework Equations

sin(a+b)=sin(a)cos(b)+sin(b)cos(a)
sin(a-b)=sin(a)cos(b)-sin(b)cos(a)

The Attempt at a Solution

Me and four of my classmates have tried to do this proof and it kicked our ***.
Please help.

 

[Mark44]

Homework Statement

sin (x) + sin (3x) + sin (5x) + sin (7x) = 4cos(x)cos(2x)sin(4x)

Homework Equations

sin(a+b)=sin(a)cos(b)+sin(b)cos(a)
sin(a-b)=sin(a)cos(b)-sin(b)cos(a)

The Attempt at a Solution

Me and four of my classmates have tried to do this proof and it kicked our ***.
Please help.

Here's what worked for me.
sin(x) + sin(3x) + sin(5x) + sin(7x) = sin(2x - x) + sin(2x + x) + sin(6x -x) + sin(6x + x)

Expand the terms on the right side, and several terms will drop out. You will need to apply the same trick again.