How do I find inverse tangent of 2/3 using a triangle? I am trying to find the inverse tangnet of 2/3 without using a calculator. 
I drew a triangle (see attached). I'm blanking out on how to find the inverse tangent since it is not an exact value that is known (pi/6, pi/4, pi/3, pi/2).
Help!


There is no real "simple form" for $\arctan(2/3)$.  You have set up the triangle nicely, but there's not much you can do from this point except a numeric approximation (e.g. Taylor Series).  
For this integral problem, it's probably best just to leave this as $\arctan(2/3)$, or if that's too much writing, just call it some unclaimed constant (e.g. $\alpha$).
