find the correlation coefficient of two random variables after the same function transformation

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we have two random variables: U1 and U2 follow uniform distribution between 0 and 1:

U1 ~ U(0,1), U2 ~ U(0,1)

and correlation: corr(U1,U2) = ρ

covariance : cov(U1,U2) = corr(U1,U2)/12

Then we do the following transformation: L1 = -ln(1-U1), L2 = -ln(1-U2)

How to calculate the correlation coefficient or the covariance between L1 and L2? Please help!