/sci/ - Science & Math

I have what is supposed to be a fairly straightforward exercise in my calculus book, I assume. (This isn't homework, I'm just a neet trying to learn calculus.)

So the problem is to find the value of h that maximizes the angle ß (beta in case the ascii breaks in the post.)
a and b are known, theta and beta unknown. (See pic related)

So I tried to write beta as a function of h so that I could maximize it, but I got an expression in terms of arctan:
theta = arctan(a/h)
beta + theta = arctan( (b+a)/h)

beta = arctan( (b+a)/h) - arctan(a/h)

I guess technically, I could differentiate that, but it looks pretty messy. Furthermore, the book hasn't shown me how to differentiate inverse trig functions yet, so I expect that I'm supposed to find a method that doesn't require taking derivatives of arctan.

I feel like there must be a basic geometric or trigonometric fact that makes the solution elegant, but I can't figure it out. Can you solve this anon?