[QUE/ME-02016] ME-PROBLEM

You are given two unit vectors \(\hat{\ell}\) and \(\hat{n}\) and angles \(\alpha,\gamma\). Find the axis \(\hat{m}\) and angle of rotation \(\beta\) such that a rotation \(R_{\hat{\ell}}(\alpha)\) followed by \(R_{\hat{m}}(\beta)\) and then by \(R_{\hat{n}}(\gamma)\) amounts to no rotation of an arbitrary vector.

Angle \(\cos\alpha=\hat{m}\cdot\hat{n}\) Clockwise rotation by \(\alpha \) about axis along \(\hat{\ell}=\hat{m}\times\hat{n}\);