Question: Einstein Tensor Calculation Approach

I've been given the task of Finding the Einstein tensor using the 4 x 4 Schwarzchild metric.  I'm starting to realize that this will be a daunting tedious task as I was told.

My question what route or approach should I take towards the different forms of the Riemann tensor which is what I will need?

Should my very first step just be calculating Christoffel Symbols of the first kind for the given metric?



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