As John mentioned you could potentially use the browser console to see the SIP messages (also you may use any network capture tool like wireshark as usual).
Please notice that a websocket call will not be any different from other type of calls in terms of SIP signalling. If you are really interested in the websocket part (HTTP handshake to upgrade the http conenction into websocket), then you will probably need a network capture tool instead of browser console. Try to use unsecure Websocket so the network capture tool may easily display all the content...