Question: Q about 'argument'

Why there is no way (except I am stupidly missing something) to let
Maple convert exp(phi*I) to argument with piecewise discussing the
input (as it is explained quite nice in ?argument)?

Even assume(-Pi < phi, phi <= Pi) does not help and results in some
arctan(sin(phi),cos(phi)) and convert(%, piecewise, phi) does not
give the desired presentation.
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