On the coordinate plane, as shown in the figure, for a point P on the circle $x ^ { 2 } + y ^ { 2 } = 1$, let $\theta \left( 0 < \theta < \frac { \pi } { 4 } \right)$ be the angle that the line segment OP makes with the positive direction of the $x$-axis. Let Q be the point where the line passing through P and parallel to the $x$-axis meets the curve $y = e ^ { x } - 1$, and let R be the foot of the perpendicular from Q to the $x$-axis. Let T be the intersection point of the line segment OP and the line segment QR, and let $S ( \theta )$ be the area of triangle ORT. When $\lim _ { \theta \rightarrow + 0 } \frac { S ( \theta ) } { \theta ^ { 3 } } = a$, find the value of $60 a$. [4 points]
On the coordinate plane, as shown in the figure, for a point P on the circle $x ^ { 2 } + y ^ { 2 } = 1$, let $\theta \left( 0 < \theta < \frac { \pi } { 4 } \right)$ be the angle that the line segment OP makes with the positive direction of the $x$-axis. Let Q be the point where the line passing through P and parallel to the $x$-axis meets the curve $y = e ^ { x } - 1$, and let R be the foot of the perpendicular from Q to the $x$-axis. Let T be the intersection point of the line segment OP and the line segment QR, and let $S ( \theta )$ be the area of triangle ORT.\\
When $\lim _ { \theta \rightarrow + 0 } \frac { S ( \theta ) } { \theta ^ { 3 } } = a$, find the value of $60 a$. [4 points]