MOD Every Other easy - but what about every 3rd

Hi,

Using MOD to determine odd rows is easy.  However, I'd like to have 3
alternating rows so need to recognize the 1st row, the 2nd row, the
3rd and start over.
So:

..blue row..
..red row..
..green row..
..blue row..
....and so on....

This didn't work:
<xsl:choose>
  <xsl:when test="position() mod 3 = 0">background_blue_fade</xsl:when>
  <xsl:when test="position() mod 2 = 0">background_green_fade</xsl:when>
  <xsl:otherwise>background_red_fade</xsl:otherwise>
</xsl:choose>