I've made it to the the final part of this question and got the expression with arctan in it:
However, I'm not sure what the final part is asking me to do. I know I've got to plug the new values into the right places, but I'm not sure what the end goal is. After putting in all the values $t_{\text{max}}$ and $U$ are both left and I don't know what to do, due to me not being able to do $\arctan(t)$ or $\tan(u)$ or anything. Anyway, any help would be appreciated.