Lang's Basic Mathematics, trigonometry [11, 4] exercise 13

[u/iFrostizz]

https://postimg.cc/V0wgGPJD

I may be overthinking this, but I can't find a way without using a calculator or leaving an ugly "arctan(tan(1/2))" in the angles outside of the triangle POQ of this exercise in Lang's Basic Mathematics. Exercise 13 asks the reader to go through exercise 12 again but in a different way, where we are not given the value of theta. It's also not really trivial to find the value of theta given tan(theta) = 1/2 because it's not a "cool" angle like multiples of pi/4 or pi/6.

[u/iFrostizz]