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I have a WMTS service URL, which gives me three layers in projection - WGS84_Pseudo-Mercator (tileMatrixSet). It's very easy to add them using this guide -> https://openlayers.org/en/latest/examples/wmts.html . But I also need to add layer in "ETRS-TM35FIN" TileMatrixSet - as I understand ETRS-TM35FIN is equal to EPSG:3067.

First solution that I found was to use raster reprojection from official docs http://openlayers.org/en/master/doc/tutorials/raster-reprojection.html but I DON'T want to change my View and set New View with another projection, because I have a lot of WFS layers with objects on the map and when I will change view to EPSG:3067 they all will disappear, because they live in EPSG:3857 system.

How could I load this layer in ETRS-TM35FIN (EPSG:3067) into my map with EPSG:3857 projection?

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If it's possible, use Capabilities File: https://openlayers.org/en/latest/examples/wmts-layer-from-capabilities.html

First, try to display it in it's source projection. Then, OpenLayers should be able to reproject it to any other projection defined with proj4

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