Trig equation word problem.

TN17

1. The problem statement, all variables and given/known data

Sorry for the long intro:

An object is propelled up at angle theta 45 deg. < theta < 90 deg. to the horiz. with initial vel. of V0 m/s. from the base of a plane that makes an angle of 45 deg. with the horiz.
If air resistance is ingored, the distance, R, travelled by the object up the inclined plane, is
R = V^2(sqrt 2)/ 32 (2sinthetacostheta - 2cos^2theta

Question
You are asked to find the angle that maximizes R by solving equation
2sinthetacostheta + 1 - 2sin^2theta = 0
Solve for theta.

2. Relevant equations
Not really any equations, just solving.

3. The attempt at a solution
I tried to continue with this, but I don't know what to do when there are two different identities.

Would I factor?

Mentallic

Do you know what sin(2x) and cos(2x) equal in terms of cosx and sinx?

TN17

Well, sin(2x) = 2sinxcosx
and cos(2x) = 2cos^x - sin^2x or 2cos^2x - 1 or 1- 2sin^2x
Is that what you mean?

Mentallic

Yes, so do you see how you can change your equation in terms of sin(2x) and cos(2x)?

Now how would you go about solving something like sin(2x)=cos(2x)
You don't need to worry about the 2x for the moment, you can just think of it as any other variable angle.