Select distinct multiple columns with one result column

I have a table like the following:

CREATE TABLE aschema.atable
 (
  id       BIGSERIAL,
  col_a    aschema.anenum,
  col_b    aschema.anenum,
  col_c    aschema.anenum
)

and I would like to do something like

SELECT DISTINCT unnest(array_agg(col_a, col_b, col_c)) as anenum_value
  FROM aschema.atable
  WHERE anenum_value IS NOT NULL

but I do not know if it makes sense.
Maybe with an index over each of the three column I can simply select independently the three columns like that:

SELECT DISTINCT value FROM (
SELECT col_a as value
  FROM aschema.atable  WHERE col_a IS NOT NULL
UNION
SELECT col_b as value
  FROM aschema.atable  WHERE col_b IS NOT NULL
UNION
SELECT col_c as value
  FROM aschema.atable  WHERE col_c IS NOT NULL
)

But I am not sure about the performance.

Actually I have rows like

id  col_a  col_b  col_c
1   ABD    CDE    XYZ
2   CDE    null   null
3   ABD    null   null
3   FGH    LMN   null

And I expect as a result

ABC
ABD
CDE
FGH
LMN
XYZ

Any recommendation and good example?

SELECT DISTINCT value FROM (
SELECT col_a as value
  FROM aschema.atable  WHERE col_a IS NOT NULL
UNION
SELECT col_b as value
  FROM aschema.atable  WHERE col_b IS NOT NULL
UNION
SELECT col_c as value
  FROM aschema.atable  WHERE col_c IS NOT NULL
)

The UNION there is UNION [DISTINCT]. You don't need to wrap it in SELECT DISTINCT. Though the previous pattern may be faster if it matters if you do UNION ALL, and wrap that in one SELECT DISTINCT FROM ()

SELECT col_a as value
  FROM aschema.atable  WHERE col_a IS NOT NULL
UNION
SELECT col_b as value
  FROM aschema.atable  WHERE col_b IS NOT NULL
UNION
SELECT col_c as value
  FROM aschema.atable  WHERE col_c IS NOT NULL

Why doesn't that work to do what you want?

If you ever find yourself writing a query like this though, I would think the problem would be in the schema itself.

StackExchange Database Administrators Q#162788, answer score: 3