Since the scale is irrelevant, let the height of the triangle be 1. The length of the green segments is x, and the remaining bit of the right triangle's base is y. Then:

2cos30=2x+y

1=x+y

tan(45-t)=y=1-x

x=2cos30-1

tan(45-t)=2-2cos30

The rest is number crunching.