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I wasn't sure what to do with the sin(dθ), so I used the small angle approximation of sin(dθ) = dθ. I would think this would be a perfect approximation because dθ is of infinitesimal size, but I'm not sure. I got the right answer, but I just wanted to make sure that this is a safe thing to do in general, or if I just got lucky.

(Sorry if this is the wrong forum, this is my first post here)