Christoffel Symbol on a Spherical Metric

\[ds^2 = r^2 \, d\theta^2 + \dfrac{1}{1+r^2} \sin^2 (\theta) \, d\phi^2.\]

A strange metric on a sphere of radius \(r\) is given by the invariant interval as described above.

Compute the Christoffel symbol \(\large \Gamma^{\phi}_{\phi \theta}\).

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