I have a square matric $H = (ABC)(ABC)^H$ where $A$ and $C$ are complex Gaussian matrices with some correlation matrices and $B$ is a diagonal matrix with entries $e^{j \theta}$ is the diagonal elements such that each $\theta$ is uniformly chosen from $[0, 1]$, Do you have any idea about the distribution of determinant of this matrix? i.e., $\text{det}[H] \sim ?$

I have a square matric $H = (ABC)(ABC)^H$ where $A$ and $C$ are complex Gaussian matrices with some correlation matrices and $B$ is a diagonal matrix with entries $e^{j \theta}$ on the diagonal such that each $\theta$ is uniformly chosen from $[0, 1]$. Do you have any idea about the distribution of the determinant of this matrix, i.e., $\det[H] \sim {?}$