Spectral radius stability condition for block matrix

Question

Let $X\in\mathbb{C}^{n\times n}$ and $a,\theta>0$. Define \begin{equation} A\triangleq\left[\begin{array}{cc}2(\cos\theta) I_n-a {\rm Re~}(e^{\jmath\theta}X)&a {\rm Re~}X-I_n\\I_n&0_n\end{array}\right]\in\mathbb{R}^{2n\times 2n}. \end{equation}

I am trying to find conditions on $X$ and $a$ such that all eigenvalues of $A$ are inside open unit disk. Any idea?