The ideology can not inspire the world in the way [ that the Western love of freedom, liberty, and justice inspires the world ] ].
The ideology can not inspire the world in the way [ how the Western love of freedom, liberty, and justice inspires the world ] ]. *論理としての文法で考えればこれが基本だよ。ただ慣用的にthatを使っているだけ。 The ideology can not inspire the world in the way. + The Western love of freedom, liberty, and justice inspires the world in a way. in a wayは関係副詞のhowに変わって従属節の頭に出る