Worked examples of Lie derivative

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I'm trying to find the Lie derivative of a 2 form $\sin(\theta)d\theta d\phi$ with respect to a vector field given in a differential basis and I think the way to go here is to use Cartan's formula but I'm not sure how to do that. I can't find any worked examples in any differential textbook or online, everything seems to focus on proving identities not performing actual calculations. Can somebody point me to a useful resource?