You have in your possession a rotation of the sphere about an axis \(l\) through an angle \(\alpha\neq 0\).
Consider the following funny rules. Suppose you have a rotation \(r_1\) through an angle \(\theta\) around an axis \(m\) and a rotation \(r_2\) through an angle \(\theta'\) around an axis \(m'\). You can add to your possession each of the below:
the rotation \(r_1^{-1}\) through \(-\theta\) around \(m\);
the rotation \(r_2r_1\) obtained by doing \(r_1\) and then \(r_2\);
the rotation \(g^{-1}r_1g\), where \(g\) is any rotation of the sphere.
Can you get all the rotations of the sphere?