Arc 1960 / UTM zone 36S to Lat Long for Google Maps

Question

I have this coordinate (778597.3125000001, 9148353). I am told this coordinate is Arc 1960 / UTM zone 36S.

When I go here: https://epsg.io/21036 and click "Get Position on Map" and enter in the above utm coordinates, it places the point in the correct place on the map (At the corner of a field).

What kind of transform/projection do I have to do to make it Lat Long, and then go to the same point in Google Maps?

I have tried various ways but seem to end up 400 - 200m diagonal offset.

The correct lat long should be: Lat: -7.699944 Long: 35.5262575 (corner of the field, see link below):

https://www.google.com/maps/place/7%C2%B041'59.8%22S+35%C2%B031'34.5%22E/@-7.6999387,35.5240688,1108m/data=!3m2!1e3!4b1!4m5!3m4!1s0x0:0x0!8m2!3d-7.699944!4d35.5262575

I am using DotSpatial.

            var Arc1960UTMZone36S = KnownCoordinateSystems.Projected.UtmOther.Arc1960UTMZone36S; 
            Arc1960UTMZone36S.AuthorityCode = 21036;

            var WGS1984 = KnownCoordinateSystems.Geographic.World.WGS1984;
            //4326 google earth  
            //3857 for google maps
            WGS1984.AuthorityCode = 3857;

            double[] xy = new double[2] { 778597.3125000001, 9148353 };
            double[] z = new double[1] { 0d };

            Reproject.ReprojectPoints(xy, z, Arc1960UTMZone36S, WGS1984, 0, 1);

            var latitude = xy[1];
            var longitude = xy[0];

            Debug.WriteLine($"Lat: {latitude} Long: {longitude}");

Would anybody know why it is offset?

Answer 1

The solution was to use proj4 string instead of the Known Coordinate System.

Instead of

var Arc1960UTMZone36S = KnownCoordinateSystems.Projected.UtmOther.Arc1960UTMZone36S; 
Arc1960UTMZone36S.AuthorityCode = 21036;

Use

String proj4_21036_str = "+proj=utm +zone=36 +south +ellps=clrk80 +towgs84=-160,-6,-302,0,0,0,0 +units=m +no_defs";    
ProjectionInfo proj21036 = ProjectionInfo.FromProj4String(proj4_21036_str);

but I don't know why.