This is my first time, so be gentle.  Although there are already plenty of tabs for A Perfect Circle?s ?3 
none of them resemble the way Billy plays it.  At a live show, I saw him starting at the 3rd fret.  I 
around with this, and here?s what I came up with:

tune down one whole step (2 frets)
Pick every chord in the same pattern.  You should be able to figure it out with the recording.

Intro
|------------------------------------|
|--3----7----3----10----7----3----8--|
|--0----0----0-----0-----0----0----0-|
|------------------------------------|
|--3----7----3----10----7----3----8--|
|------------------------------------|

Verse
|-------------------------------|
|--3----5----6-----3----5----8--|
|--0----0----0-----0----0----0- |
|-------------------------------|
|--3----5----6-----3----5----8--|
|-------------------------------|

Distortion kicks in
|--------------------------------|
|--------------------------------|
|--8--8--8--8--8 / 6--6--6--6--6-|
|--------------------------------|
|--6--6--6--6--6 / 4--4--4--4--4-|
|--------------------------------|

I don?t know... Maybe that?ll help somebody.  By the way, they?re supposedly going to come out with at 
2 more albums.  I hope so!  I don?t think that ?Wake the Dead? song is A Perfect Circle, though.  And check 
Civilian!  It?s Chris Cornell of Soundgarden singing and Tom, Tim, and Brad of Rage Against the Machine.  Rumor is they?re not going to release it, but it?s still damn good stuff!

?You?ll never go doody?  That?s what you think...?  - Frank Zappa