As shown in the figure, there is a rhombus ABCD with side length 1. Let E be the foot of the perpendicular from point C to the extension of segment AB, let F be the foot of the perpendicular from point E to segment AC, and let G be the intersection of segment EF and segment BC. If $\angle \mathrm { DAB } = \theta$, let the area of triangle CFG be $S ( \theta )$. What is the value of $\lim _ { \theta \rightarrow 0 + } \frac { S ( \theta ) } { \theta ^ { 5 } }$? (Here, $0 < \theta < \frac { \pi } { 2 }$) [4 points] (1) $\frac { 1 } { 24 }$ (2) $\frac { 1 } { 20 }$ (3) $\frac { 1 } { 16 }$ (4) $\frac { 1 } { 12 }$ (5) $\frac { 1 } { 8 }$
As shown in the figure, there is a rhombus ABCD with side length 1. Let E be the foot of the perpendicular from point C to the extension of segment AB, let F be the foot of the perpendicular from point E to segment AC, and let G be the intersection of segment EF and segment BC. If $\angle \mathrm { DAB } = \theta$, let the area of triangle CFG be $S ( \theta )$.
What is the value of $\lim _ { \theta \rightarrow 0 + } \frac { S ( \theta ) } { \theta ^ { 5 } }$? (Here, $0 < \theta < \frac { \pi } { 2 }$) [4 points]\\
(1) $\frac { 1 } { 24 }$\\
(2) $\frac { 1 } { 20 }$\\
(3) $\frac { 1 } { 16 }$\\
(4) $\frac { 1 } { 12 }$\\
(5) $\frac { 1 } { 8 }$