Do you need the implicit function theorem? Can you give an explicit charts?
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closed as too localized by Qiaochu Yuan, Deane Yang, Mariano SuárezAlvarez♦, Angelo, Willie Wong Jan 22 '11 at 16:33This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question. 


Euler angles give the parametrization and the charts. 

