Wolfram Alpha: The limit is zero

Me: Really? Why? *Clicks show steps*

Wolfram Alpha: The limit IS zero dammit, stop being so curious...

This is bad news for me though

I'm supposed to find an upper bound for

on the square with vertices

This is then supposed to vanish when multiplied by the perimeter of the square as N goes to infinity.

My upper bound times perimeter was of that form and since Wolfram Alpha was encouraging I assumed I had got it right...

Serves me right for not posting the whole question...

Any ideas? Sorry this might be a bit tough...

My first attempt was to write cot in terms of exp and use the triangle inequality...