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In triangle $ABC$ the points $D,U,L$ on $BC$ are respectively the foot of the perpendicular from $A$ onto $BC$,the point where the internal bisector of angle $A$ meets $BC$,and the midpoint of $BC$.If the angles $\angle BAD,\angle DAU,\angle UAL,\angle LAC$ are all equal,determine the angles of the triangle $ABC$.

$\angle A=90$
$\angle B=22.5$
$\angle C=67.5$