Prove that 3 by 3 orthogonal matrix is unitarily similar to certain rotation matrix

Question

Suppose that we have an 3 by 3 orthogonal matrix $A$ with determinant $1$. I want to prove that $A$ is unitarily similar to matrix $\begin{bmatrix}cos\theta &-sin\theta & 0 \\ sin\theta & cos\theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$. I am stuck on this, my idea is to utilize the fact that $A$ has $1$ as an eigenvalue and it is unitarily diagonalizable.