Let $ABC$ be a triangle whose angles measure $A$, $B$, $C$, respectively.  Suppose $\tan A$, $\tan B$, $\tan C$ form a geometric sequence in that order. If $1\le \tan A+\tan B+\tan C\le 2015$, find the number of possible integer values for $\tan B$.  (The values of $\tan A$ and $\tan C$ need not be integers.)

[i] Proposed by Justin Stevens [/i]