How to prove the z component of angular momentum?, chemistry homework help

So we know Lz, the angular momentum component , equals (Hbar/i)(d/dθ). How do we show this using the relationships that

Lz = (hbar/i)[x(d/dy) -y(d/dx)], x = rsinθcosφ, y = rsinθsinφ, and z = rcosθ. (d/dy) and (d/dx) are the linear momentum for its respective component. How do I go about doing this? I have tried substituting x and y into the Lz equation followed by deriving the y equation with respect to θ and φ and substituting that in for (d/dy) and doing the same process for (d/dx) but cannot prove that Lz = (hbar/i)(d/dθ). Am I on the right track? Any help is appreciated!

 

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