Couldn't publish WMTS for neither 4326 nor 900913

[kanerlevent]

I am trying to add the default WMTS Italy mosaic that can be found in GeoServer by default (nurc:mosaic, namely) to my map via Leaflet by tweaking the code shared here.
I get the WMTS link by simply right clicking on GeoServer's Web Admin page WMTS 1.0.0 and copy the link location. Here it is: http://localhost:8081/geoserver/gwc/service/wmts?REQUEST=GetCapabilities
And here is my code:

// The WMTS URL
var url = "http://localhost:8081/geoserver/gwc/service/wmts?REQUEST=GetCapabilities";

var italy = new L.TileLayer.WMTS( url ,
{
layer: 'nurc:mosaic',
style: "",
tilematrixSet: "EPSG:900913",
format: "image/png"
}
);
var map = L.map('map').setView([37, 24], 4);

L.control.scale({'position':'bottomleft','metric':true,'imperial':false}).addTo(map);

var osm = L.tileLayer('http://{s}.tile.osm.org/{z}/{x}/{y}.png', {
attribution: '© OpenStreetMap'
}).addTo(map);

var baseLayers = {
"ItalyWMTS" : italy,
"OpenStreetMap": osm
};

L.control.layers(baseLayers).addTo(map);

It didn't work.

I also checked if the nurc:mosaic has the EPSG:900913 defined, it has. ( I checked it from the GeoServer's Web Admin Page - Tile Layers - Tile Caching - Gridset, there are gridsets for both EPSG 4326 and EPSG 900913).
I couldn't manage to get it work with 4326 too

[zigacernigoj]

It's because the rows and columns are computed differently.
You would want to check if it is EPSG:4326 and compute rows and cols the way that is described here.

I will try it "tomorrow" and will tell if it's doable.