Extend PostGIS polygon with 2 new points

I have a PostGIS polygon which has to be extended using two points like on the picture:

My original polygon is: POLYGON((10 20,10 10,20 10,20 20,10 20))

The points I would like to extend the polygon with: POINT ( 20 30 ) and POINT ( 10 30 )

It’s very important that I would like to insert the Point2 as the first and the last point of the polygon. The Points1 should be in the last but one position. So the position of the new points is crucial.

What do you think, what is the best method to do this? Any suggestions?

UPDATE: I’ve find a solution, it works, but a little bit complicated:

SELECT ST_MakePolygon(ST_AddPoint(ST_AddPoint(ST_AddPoint(ST_RemovePoint(ST_ExteriorRing( ST_GeomFromText('POLYGON((10 20,10 10,20 10,20 20,10 20))')),
ST_NPoints(ST_GeomFromText('POLYGON((10 20,10 10,20 10,20 20,10 20))'))-1),ST_MakePoint(20,30)),ST_MakePoint(10,30),0),
    ST_MakePoint(10,30)));