Google APIs Client Library for PHPでgd:etagを取得する ref: http://qiita.com/sakadon/items/34552fb99669d6879466

file0.php

$sheet_id = '#########';
$request = new Google_Http_Request(
    "https://spreadsheets.google.com/feeds/worksheets/{$sheet_id}/private/full?alt=json",
    "GET",
    array(
        "Authorization" => "Bearer {$this->token}",
        "GData-Version" => "3.0"
    )
);

file1.php

stdClass Object
(
    [version] => 1.0
    [encoding] => UTF-8
    [feed] => stdClass Object
        (
            [xmlns] => http://www.w3.org/2005/Atom
            [xmlns$openSearch] => http://a9.com/-/spec/opensearch/1.1/
            [xmlns$gs] => http://schemas.google.com/spreadsheets/2006
            [xmlns$gd] => http://schemas.google.com/g/2005
            [gd$etag] => W/"AAAAAAAAAAAAAAAAAAAAAAA."
            [id] => stdClass Object
                (
                    [$t] => https://spreadsheets.google.com/feeds/worksheets/シートID/private/full
                )
...

file2.xml

<entry xmlns="http://www.w3.org/2005/Atom" xmlns:gs="http://schemas.google.com/spreadsheets/2006" xmlns:gsx="http://schemas.google.com/spreadsheets/2006/extended" gd:etag='"AAAAAAAAAAAAAAAAAAAAAAA."'>
    <category scheme="http://schemas.google.com/spreadsheets/2006" term="http://schemas.google.com/spreadsheets/2006#list"/>
    <id>{$lineid}</id>
    <link rel="self" type="application/atom+xml" href="{$selfhref}"/>
    <link rel="edit" type="application/atom+xml" href="{$edithref}"/>
    <gsx:headname>Update</gsx:use>
</entry>

file3.php

$request = new Google_Http_Request(
        $edithref,
        "PUT",
        array(
            "Authorization" => "Bearer {$accessToken}",
            "Content-Type" => "application/atom+xml",
            'GData-Version' => "3.0"
        ),
        $postBody // <= ↑のXML
    );