First, let's write down the given matrix A:
$$
A = \begin{bmatrix}
\cos\theta & 0 & \sin\theta \\
0 & 1 & 0 \\
-\sin\theta & 0 & \cos\theta
\end{bmatrix}
$$
Now, let's find the inverse of matrix A, denoted as $A^{-1}$:
$$
A^{-1} = \begin{bmatrix}
\cos\theta & 0
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