How to solve this orthogonal matrix equation?

Question

I have an equation like this: $ A = R^T * B * R $.

Actually, the problem should be like this: $ argmin\sum_{i=0}^{n-1}(q_i^T*R^T*B*R*p_i)$. It's similar to the above equation. $q_i, p_i$ are known.

$ A, R, B $ are orthogonal matrices, matrix $ A $ and $ B $ are known. All of these matrices are real, $ 3 × 3 $.

How to obtain R or give me some tips?

Thanks in advance.