Characters (<) and (>) escaped incorrectly in xml attributes

For XML document :

The left angle bracket (<) MUST NOT appear in their literal form,
 [...] they MUST be escaped using [...] the string &lt;". 
The right angle bracket (>) [...] MUST be escaped using "&gt;"

Full source : https://www.w3.org/TR/xml11/#syntax

Test snippet:

const document = (new DOMParser).parseFromString('<root attr="&lt;&gt;"></root>', 'text/xml');

assert(document.toString(), '<?xml version="1.0" encoding="utf-8"?><root attr="&lt;&gt;" />');

Expected: <?xml version="1.0" encoding="utf-8"?><root attr="&lt;&gt;" />
Got instead: <?xml version="1.0" encoding="utf-8"?><root attr="<>" />

Note :

• The HTML parser must not changed and does not have the same behavior
• Only the .toString function must escaped, the getAttribute("attr") must continue to provide unescaped characters (<) and (>)

Start with the DOMParser and XML toString behavior shown in the supplied test snippet, reproducing it first. Done means XML serialization escapes angle brackets in attribute values, getAttribute("attr") still returns unescaped characters, and HTML parsing remains unchanged.