Finding Trig functions using the Triangle Method (due tommorow)

Problem:

That -1 is suppose to represent the inverse. Basically, I've narrowed things down the 4th quadrant (ASTC), and I've reduced the problem down to:

Alright, we also have Opposite over Adjacent as well (TOA), so therefore what would we be working with to create the formula (Pythagorean Theorem) needed to solve the question? Or to make things more precise, how exactly would this triangle and equation look if everything were to be plugged in correctly given the details I have gathered about the problem? Furthermore, what roll is the secant function going to play when I finally solve the inside of the inverse tangent function?

And finally, what is the difference between what is being asked of the problems... one is asking for the exact evaluation, while the other is asking for an identity. Our professor hasn't gotten much into depth of any of this stuff, but I got a worksheet due tomorrow on it, so I'm kind of on my own here. And I also apologize if I'm not clear at all on my explanations, as I'm extremely tired as I type this. I probably should used some more mathematical terminology, but my mind is so worn-out right now it's a pretty rough thing to come by.