Show that the map RX,π:S2→S2 given by (a,b,c)→(a,−b,−c) (rotation about the x-axis by π radians) and the map \(T_{X,\pi}\colon \hat{\mathbb{C}}\to \hat{\mathbb{C}}...Show that the map RX,π:S2→S2 given by (a,b,c)→(a,−b,−c) (rotation about the x-axis by π radians) and the map TX,π:ˆC→ˆC given by z→1/z are conjugate transformations with respect to stereographic projection.