In HHL algorithm, how to find the angle of rotation of ancilla qubits?

In HHL algorithm, after the quantum phase estimation, what is the angle of rotation i.e. what is the value of $$\theta$$ in R$$_y$$($$\theta$$) that is used in rotating ancilla qubit? How to find this angle of rotation without knowing the eigenvalues of matrix $$A$$? Is there any general method to find this angle of rotation for any $$n$$x$$n$$ Hermitian matrix $$A$$?

• note that you can use equations in posts via mathjax, see e.g. quantumcomputing.meta.stackexchange.com/q/49/55 – glS Mar 17 at 11:12
• That's why it's controlled off "register". That tells you (approximately) the eigenvalue and so you compute the rotation angle based upon that. – DaftWullie Mar 17 at 11:55
• @glS , thanks for the suggestion. I have updated the question. – quankid Mar 17 at 11:56
• @DaftWullie Can you explain in detail what you want to say. Better to explain with an example. – quankid Mar 17 at 12:00