Looking at the problem from the other end, i.e. as a user who sees hollow squares for ⟨
(but also ⟨
and ⟩
), I found a solution for IE7 (on Windows XP):
In the Internet Properties (Sorry, I have only a German version here, so I don't know if this is the correct name.), go to Fonts, and set the text font to Arial Unicode MS or Lucida Sans Unicode.
Strange enough, even if a page doesn't use that font, just the setting causes IE7 to correctly interpret those HTML named entities.
Edit: Lucida Sans Unicode doesn't work for all entities. E.g., ∠
or ↩
display ok but ⟨
and ⟩
not.