## When is the Identity tanAtanBtanC=tanA+tanB+tanC Valid?

If
$A, \: B, \: C$
are the angles of a triangle, then
$A+B+C=180$
and
$tanAtanBtanC=tanA+tanB+tanC$
.
Is it true though that if
$tanAtanBtanC=tanA+tanB+tanC$
. then
$A, \: B, \: C$
are then angles of a triangle?
Not it is not. Then tangent function repeats every 180 degrees, so we can add multiples of 180 to any of
$A, \: B, \: C$
or all of then and the identity would still hold. The necessary and sufficient condition for
$A, \: B, \: C$
to satisfies the identity is than
$A+B+C=180k,$
where
$k$
is any whole number, positive, negative or zero.