The Dirichlet integral is one of the coolest integrals in existence and its various solution developments are indeed mesmerising!
Comment down below which technique you liked best
Jordan's lemma:
https://youtu.be/ncmbeIVjrDg
https://youtu.be/12bBMiwOC94
Series expansion for csc function:
https://youtu.be/mL3ftmldMow
Lobachevsky's formula:
https://youtu.be/Bq5TB6cZNng