Hence solve the equation \(\sin ^ { 4 } \theta - \cos ^ { 4 } \theta = \frac { 1 } { 2 }\) for \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).
\(6 \quad A\) is the point \(( a , 2 a - 1 )\) and \(B\) is the point \(( 2 a + 4,3 a + 9 )\), where \(a\) is a constant.
Find, in terms of \(a\), the gradient of a line perpendicular to \(A B\).
Given that the distance \(A B\) is \(\sqrt { } ( 260 )\), find the possible values of \(a\).