You are half way there. All you need to do is to get the map bounds and then extract (and properly use) the coordinates of the corners.
var bounds = map.getBounds();
var ne = bounds.getNorthEast(); // LatLng of the north-east corner
var sw = bounds.getSouthWest(); // LatLng of the south-west corder
You get north-west and south-east corners from the two above:
var nw = new google.maps.LatLng(ne.lat(), sw.lng());
var se = new google.maps.LatLng(sw.lat(), ne.lng());
Just keep in mind that the map has to be already initialized, otherwise the map bounds are null or undefined.
If you want to be updated about every change of the viewport, use idle
event listener:
google.maps.event.addListener(map, 'idle', function(ev){
// update the coordinates here
});
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