Show that the equation
$$\frac { 1 } { \sin \theta + \cos \theta } + \frac { 1 } { \sin \theta - \cos \theta } = 1$$
may be expressed in the form \(a \sin ^ { 2 } \theta + b \sin \theta + c = 0\), where \(a\), \(b\) and \(c\) are constants to be found.