Tuum can be accusative, or nominative, because "munus, -eris" is a neutral noun. That means that "munus tuum" is linked to the object or to the subject of "captus".
As there isn't the context, I cannot be sure, so I give the two options. But, in my opinion, the second is the correct, as I think this phrase come from a text in first person.
Thanks Mistaya, when you have several translation alternative, only keep the best one in the main field and the others in the comments. I've edited the translation.
お気に入りの翻訳
