Need to solve solutions for [0,2π)

Problem: Sin x + cos X=1. What I did was square both side.

SinX^2+2sinXcosX+cosX^2=1. It's the Middle term that is really throwing me off. I know that I need to get either all cos or sin. I know how to change Cosx^2 into 1-sinx^2. Just not sure where do go after that.