Problem:

Here is a triangle I have drawn:

Hi I am having a little difficulty figuring out how to solve this problem near the end.

After I used trig sub and integrated it, I get to this point, 20θ + 10sin(2θ). Now at this point I know the θ next to the 20 will be inverse sin(y/2). But figuring out the 10sin(2θ) has gotten me confused. How do we solve for theta in that case?