As shown in the figure, there are two circular disks with distance between centers $\sqrt { 3 }$ and radius 1, and a plane $\alpha$. The line $l$ passing through the centers of each disk is perpendicular to the planes of the two disks and makes an angle of $60 ^ { \circ }$ with plane $\alpha$. When sunlight shines perpendicular to plane $\alpha$ as shown in the figure, what is the area of the shadow cast by the two disks on plane $\alpha$? (Note: the thickness of the disks is negligible.) [4 points] (1) $\frac { \sqrt { 3 } } { 3 } \pi + \frac { 3 } { 8 }$ (2) $\frac { 2 } { 3 } \pi + \frac { \sqrt { 3 } } { 4 }$ (3) $\frac { 2 \sqrt { 3 } } { 3 } \pi + \frac { 1 } { 8 }$ (4) $\frac { 4 } { 3 } \pi + \frac { \sqrt { 3 } } { 16 }$ (5) $\frac { 2 \sqrt { 3 } } { 3 } \pi + \frac { 3 } { 4 }$
As shown in the figure, there are two circular disks with distance between centers $\sqrt { 3 }$ and radius 1, and a plane $\alpha$. The line $l$ passing through the centers of each disk is perpendicular to the planes of the two disks and makes an angle of $60 ^ { \circ }$ with plane $\alpha$. When sunlight shines perpendicular to plane $\alpha$ as shown in the figure, what is the area of the shadow cast by the two disks on plane $\alpha$? (Note: the thickness of the disks is negligible.) [4 points]\\
(1) $\frac { \sqrt { 3 } } { 3 } \pi + \frac { 3 } { 8 }$\\
(2) $\frac { 2 } { 3 } \pi + \frac { \sqrt { 3 } } { 4 }$\\
(3) $\frac { 2 \sqrt { 3 } } { 3 } \pi + \frac { 1 } { 8 }$\\
(4) $\frac { 4 } { 3 } \pi + \frac { \sqrt { 3 } } { 16 }$\\
(5) $\frac { 2 \sqrt { 3 } } { 3 } \pi + \frac { 3 } { 4 }$