The second part of the problem:

Let the transformation from (X,Y) -> (R,θ) be defined as

$\displaystyle R = \sqrt{(X-\mu)^2+(Y-\mu)^2}$

$\displaystyle \theta=$

$\displaystyle arctan \left ({(Y-\mu) \over (X-\mu)} \right ), \text{if }X \ge \mu$

$\displaystyle -\pi + arctan \left ({(Y-\mu) \over (X-\mu)} \right ), \text{if }X < \mu; Y < \mu$

$\displaystyle \pi + arctan \left ({(Y-\mu) \over (X-\mu)} \right ), \text{if }X < \mu; Y \ge \mu$

find the joint density and marginal densities.

So far on this part I have it solved for X and Y:

$\displaystyle X = \sqrt{R^2 - (Y-\mu)^2} + \mu$

$\displaystyle Y = tan(\theta)(X-\mu) + \mu$

I tried plugging in the equations into each other but I don't know how to get rid of the tan(). Any help is appreciated.