Different identities in one equation

[TN17]

1. Homework Statement

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, traveled 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. Homework 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?

 

[LCKurtz]

Try using the identities for sin(2θ) and cos(2θ).