I want to solve:

2arctan(2)+arcsin(4/5).

I am doing this by setting

arctan(tan(2arctan(2)+arcsin(4/5))

and then by using the addition formula for tangens twice I get arctan(0)=0

But here is the thing, my text book want's it to be pi.

I can't see how it can since the arctan can never be anything outside [-pi/2,pi/2] right?

So what do I do wrong, anyone?