Projectile Motion Proof/Hassle

Varaia

This is a real pain and I'm getting nowhere. If you can't see the image look at the attached file.
Angle a(upper angle)=Theta Angle b(lower angle)=Beta
Prove these relations:
a) Rsin2theta+d(1+cos2theta)=(R^2)/Rnot where Rnot= ((vnot)^2)/g
b) That Rm(meaning maximum R) happens for tan2(thetamax)=Rm/d
c) 2thetamax+alpha=90 degrees
d) (Rnot^2)+2dRnot=Rm^2


For a) I'm getting down to 2costheta(Rsintheta+dcostheta)=(R^2)/Rnot
But I don't see the next step, maybe I went too far. Or do I need to include Beta somewhere? I don't think I do. There is some trig relation or relating it to the diagram that I just don't see.
All I really need is help on a)then
I can use what I know from a) to solve for b) and each one after can be done likewise however I won't get to them if I can't get a) done.
Please HELP!

Attached Thumbnails

 

OlderDan

2costheta(Rsintheta+dcostheta)=(R^2)/Rnot

R(sinthetacostheta+costhetasintheta)+2dcos^2theta)=(R^2)/Rnot

Do you remember any trig identities?

http://www.sosmath.com/trig/Trig5/trig5/trig5.html