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(2\arccos(\sqrt{1-\xi_x}), 2\pi\xi_y) \rightarrow (\theta, \phi)
(1/x, 1/y, 1/z)
\delta : X \rightarrow X \otimes X
(\epsilon \otimes id_A) \circ P (\phi) = \\
 (\epsilon \otimes id_A)(\sum e_i \otimes P_i(\phi))= \\
 \sum 1 \otimes P_i(\phi) = \\
 1 \otimes \sum P_i(\phi)
(\epsilon \otimes id_A) \circ P (\phi) = \\
 (\epsilon \otimes id_A)(\sum e_i \otimes P_i(\phi))= \\
 \sum 1 \otimes P_i(\phi) = 1 \otimes \sum P_i(\phi)