# Sum of angles in a parallelepiped

How does one show that the sum of the solid angles in a parallelepiped is $4\pi$ steradians? It's easy to see that the sum of angles in a parallelogram is $2\pi$ radians using the definition of parallel lines, but I'm having trouble generalizing this to the $3$ dimensional case.

Hint: "Tile" $3$-dimensional space with the parallelepiped.