How to solve this trig equation

[Vee9]

Homework Statement

Solve for θ.
2sinθcosθ + 1 - 2sin^2θ = 0

Homework Equations

The Attempt at a Solution

I tried factoring, but I don't know how to continue with 2 diff ID's in one equation.
I don't know how to simplify it so that everything is in terms of one similar Identity.
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[Bohrok]

Do you know any identities for 2sinθcosθ and 1 - 2sin²θ?

 

[symbolipoint]

My mistake. You meant to show sin²(theta), and I misread this.

 

[Vee9]

okay, I used 2sinxcos x and changed it to sin 2x so that I get:
-2sin^2(x) + sin2x + 1 = 0
How could I continue since I put everything in terms of sin?

 

[vela]

Find an identity for 1 - 2sin²x and use that.