Derive correlation from correlation with a shared variable

[frankQ]

Hi,

I have the following problem:
StDev(X), StDev(Y), Correlation(X, Z), Correlation(Y, Z)
I am trying to figure out if I am somehow able to derive Correlation(X, Y) from the above data, i.e., rely on each variable's (X and Y) correlation with a common third (Z) to derive the correlation of X and Y.

I can't think of a way but would welcome any suggestions.

Thanks