Detailed Solution:

The one hint square is the only square to be shaded in the top row of the top horizontal tier of blocks. Thus, Stamp 2 must be used in the right block of that tier, with its top row empty, and this determines the orientation of the left block, using Stamp 1.

Subtracting vertically, we can determine the orientation of the remaining stamp in the left most vertical tier of blocks. Note that the second horizontal tier of blocks from the top must all use Stamp 1, since every row totals three.

The bottom row in the bottom horizontal tier of blocks is supposed to have no shaded squares. The only way to make an outer row empty is to use Stamp 2.

Subtracting vertically, we can determine the orientation of the remaining stamp in the right most vertical tier of blocks. Note that the two remaining blocks in the second horizontal tier of blocks from the bottom must all use Stamp 2, according to the remaining

In the middle two vertical tiers, subtracting the blocks we have already positioned, we find that two edge columns total one. Since the upper remaining blocks must have one shaded square in those edge columns, because they will be filled with Stamp 1, the orientation of the Stamp 2 blocks can be determined.

Working vertically, we can determine the orientation of the remaining two Stamp 1 blocks.