How to diagonalize $D_1U^\dagger D_2U$ with unitary $U$ and real diagonal $D_{1,2}$

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Is there a trick to diagonalize the following expression $$D_1U^\dagger D_2U$$ such that $$D_1U^\dagger D_2U=V^\dagger D\,V$$ where $U$ is unitary and $D_1$ and $D_2$ are diagonal and real?