I want to aim a desk lamp by specifying where it should point.  P(x,y)
is where to aim the lamp, c is the length of the flexible part of the
neck, a is an additional rigid distance to the central axis of the lamp
hood, and f is the angle to bend the neck.  The initial equation was
huge and ugly, but I managed to simplify it considerably, to this form:

  (x - c/f) * sin(f) + y * cos(f) = a

But now I'm stuck.  Variables a, c, x, and y are given, and I need to
solve for f.  I plugged it into Wolfram Alpha, but it gave up.  I don't
even know if a paid subscription would find a solution, and I would
hardly use the service enough to justify a subscription anyway.  Does
anyone have an idea of how to proceed with the equation?  Or should I
gamble that Wolfram Alpha Pro can solve it and pay for one month?

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