Solving Two Problems: What Am I Doing Wrong?

[Helicobacter]

On two problems, I got the wrong answer w/ the same approach; yet I can't find my mistake...

 

[neutrino]

First problem: Although you have implicitly performed a substitution, you haven't done it completely. The integral of tan(x) is -ln(cos(x)), but that of tan(x/3) is slightly different. Use u = x/3.

Second: [Perhaps you meant to write 2ln(sin(theta/3))?] You have done the same mistake here as well.

 

[Helicobacter]

Yes, I did intend to write 2ln(sin(theta/3)). Thanks for your help