So I got this answer $-r^2\sin \theta\sin(\phi+\theta)dr d(\phi)d(\theta)$ which I think is wrong because I googled it and it must be $-r^2\sin\theta dr d\phi d\theta,$ but $\sin(\phi+\theta$) clearly is not equal to 1 so whats wrong with my calculations? If it's wrong
2026-03-29 18:50:32.1774810232
$dxdydz \to -r^2\sin(\theta)\sin(\phi+\theta)dr d\phi d\theta$?
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You should have $z = r\cos\theta$ not $z = r\cos\varphi$. For your choice of $z$ the equation $x^2 + y^2 + z^2 = r^2$ does not hold, which it should.