Let $S = \left\{ \theta \in [ 0,2 \pi ] : 8 ^ { 2 \sin ^ { 2 } \theta } + 8 ^ { 2 \cos ^ { 2 } \theta } = 16 \right\}$. Then $n ( S ) + \sum _ { \theta \in \mathrm { S } } \left( \sec \left( \frac { \pi } { 4 } + 2 \theta \right) \operatorname { cosec } \left( \frac { \pi } { 4 } + 2 \theta \right) \right)$ is equal to:\\
(1) 0\\
(2) $- 2$\\
(3) $- 4$\\
(4) 12