# How to compute $cov(\frac{1}{2}Z'AZ,\frac{1}{2}Z'BZ)$?

I want to show that $$cov(\frac{1}{2}\textbf{Z}'A\textbf{Z},\frac{1}{2}\textbf{Z}'B\textbf{Z})=\frac{1}{2}tr(AR(\theta)BR(\theta))$$

where $$A,B \in Sym(p)$$ (real symmetric $$p \times p$$ matrices) and $$\textbf{Z}= (Z_1 , \ldots,Z_p)'\sim N_p(0,R(\theta))$$

I tried to use the fact that if $$x \sim N_n (\mu, \Omega)$$ and $$A$$ is a symmetric $$n \times n$$ matrix, then $$\text{E}[x'Ax] = tr A \Omega + \mu ' A \mu.$$

but i didn't succeed. Do you have any suggestions?