Cross Variation of two stochastic processes

Question

I am currently working on a stochastic calculus exercise at the moment and I am slightly confused when it comes to finding cross variation.

We are given that the process $X_t = W_t^3$ ($W_t$ is standard Brownian Motion), and that $Y_t = sin(W_t)$.

We are then asked to find the cross variation between $Z_t$ and $U_t$, where $Z_t = Y_t^2$ and $U_t = e^{X_t}$.

I've found (I hope correctly) the Ito decomposition of $Z_t$ and $U_t$ to be given by

$dZ_t = cos(2W_t) dt + sin(2W_t) dW_t$

$dU_t = \frac{1}{2} e^{W_t} dt + e^{W_t} dWt$

I'm unsure though how to proceed and find $<U, Z>$.

Any help would be appreciated - many thanks.