Answer
See graph and explanations.
Work Step by Step
See graph; it appears there is a maximum of the slope function $y'=-csc^2x$ at $x=\pi/2$, which gives $y'=-csc^2(\pi/2)=-1$, and it appears that there is no minimum of the slope function.
The derivative will never be positive and $y'=-csc^2x\leq-1$
