I recently came across this problem and would like some clarification as to why one of the answers to theta cannot be

The problem asks to sketch two polar curves and find where they intersect, and then present those points in rectangular coordinates. I can easily see from the graph that the points are (1,0) and (-1,0). The two polar functions are,

and r = -1.

I set them equal to each other

Ok, is it r = 1 or r = -1??
So theta should be...

This is wrong:
Yet the graph tells me only pi and -pi can be the answer. I'm confused...