Need some help/advice/guidance for question 11.6 from Wald, General Relativity

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Hey,
I was reading through chapter 11 in the Wald GR book and I came across question 11.6, which i was trying to solve, but I am having difficulties getting started on the questions a) and b), as I have only just learnt about tangent vectors (and diff geometry in general) etc. and I would like to ask for some guidance at attempting to answer the question.

In particular, I am not sure how to show that the angular momentum J is independent of the sphere it is integrated over. so if you knew how to attempt this question, i would appreciate a "push into the right direction".

Thanks
 
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