Why doesn't arctan2(sqrt(a^2 + r^2)*sin(phi)*sin(th), sqrt(a^2 + r^2)*cos(phi)*sin(th)) simplify to phi or at least arctan2(sin(phi),cos(phi))?

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Why doesn't arctan2(sqrt(a^2 + r^2)*sin(phi)*sin(th), sqrt(a^2 + r^2)*cos(phi)*sin(th)) simplify to phi or at least arctan2(sin(phi),cos(phi))?

Why doesn't `arctan2(sqrt(a^2 + `

simplify to phi or at least ~~r^2)~~r^2)*sin(phi)*sin(th), sqrt(a^2 + *sin(phi)*sin(th), ~~r^2)~~r^2)*cos(phi)*sin(th))*cos(phi)*sin(th)) ~~arctan2(sin(phi),cos(phi))?~~`arctan2(sin(phi),cos(phi))`

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