Simplify of cosinus and sinus terms

Hi,

I have a calculation where I have to simplify some trogonometric terms. I did it up to here und and to here I am sure that it es correct but now I stumble. How to go on?

Target of the calculation is: $\displaystyle r^2 \sin(\Theta)$

This is the point I stumble:

$\displaystyle r^2 [ \cos(\Theta)^2 \sin(\Theta) \cos(\varphi)^2 + \sin(\Theta)^3 \sin(\varphi)^2 $ $\displaystyle + \cos(\Theta)^2 \sin(\varphi)^2 \sin(\Theta) + \sin(\Theta)^3 \cos(\varphi)^2 ]$

Whats next?

I guess I have to use that sin square plus cos square is one, but I guess here it would be wrong.

thanks

greetings