How do you figure this out What are the values of theta between 0 and 360 when tan theta -1?

This is a fairly straightforward trigonometry problem.

I'll assume you were give tan(θ)=(-1) for 0o < θ < 360o in this situation.

I strongly suggest you familiarize yourself with the unit circle. In this case, we are looking for a point on the circle where the slope between (0,0) and the point at θ is (-1). This occurs at 135o and 315o.

Short Answer: θ = {135o, 315o}