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In the diagram below, $7\text{ circles}$ of radius $2$ are externally tangent, and the centers of the outer $6\text{ circles}$ are connected to make a regular hexagon.

Mark Conkle. Created for Albert.io. Copyright 2016. All rights reserved.

What is the shaded area?

$4\pi$

$8\pi$

$12\pi$

$16\pi$

$28\pi$