MySQL COUNT() multiple columns

Question

I'm trying to fetch the most popular tags from all videos in my database (ignoring blank tags). I also need the 'flv' for each tag. I have this working as I want if each video has one tag:

SELECT tag_1, flv, COUNT(tag_1) AS tagcount 
  FROM videos 
 WHERE NOT tag_1='' 
 GROUP BY tag_1 
 ORDER BY tagcount DESC LIMIT 0, 10

However in my database, each video is allowed three tags - tag_1, tag_2 and tag_3. Is there a way to get the most popular tags reading from multiple columns?

The record structure is:

+-----------------+--------------+------+-----+---------+----------------+ 
| Field           | Type         | Null | Key | Default | Extra          | 
+-----------------+--------------+------+-----+---------+----------------+ 
| id              | int(11)      | NO   | PRI | NULL    | auto_increment | 
| flv             | varchar(150) | YES  |     | NULL    |                | 
| tag_1           | varchar(75)  | YES  |     | NULL    |                | 
| tag_2           | varchar(75)  | YES  |     | NULL    |                | 
| tag_3           | varchar(75)  | YES  |     | NULL    |                | 
+-----------------+--------------+------+-----+---------+----------------+ 

Answer 1

select tag, flv, count(*) as tag_count
from (
  select tag_1 as tag, flv from videos
  UNION
  select tag_2 as tag, flv from videos
  UNION
  select tag_3 as tag, flv from videos
) AS X

I think that will do it, although there will be double-counting if any record has the same values for two of the tags.

UPDATE: added AS X.