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Your starting equation is
    sin(A) = -cos(A)   and  you consider it in this diapason  -180° < A < 180°.
Divide both sides of the equation by cos(A).  You will get
    tan(A) = -1   and   -180° < A < 180°.
It has two solutions in the given interval  A = -45° and  A = 135°.    ANSWER
Solved, explained and completed.