This is a silly question. It asks one to do something that can't be done.
The sentence
- I must go and look for my brothers.
is Intransitive, but Passive can only apply to a Transitive clause.
The Passive rule promotes the direct object to subject, demotes the old subject to an optional object of by, and adds the auxiliary verb be before the past participle form of the main transitive verb. Like this:
- Marie shot my cousin. == Passive => My cousin was shot (by Marie).
But if the clause isn't transitive, there isn't a direct object to promote, and other noun phrases don't usually work.
- Mary slept all day. but not *All day was slept (by Mary).
Sometimes prepositional objects can be passivized, if the preposition is one that makes a transitive verb out of an intransitive one, like look (at) or listen (to)
- We must look at/listen to that again. == Passive => That must be looked at/listened to again.
But that's rarely the case, so most prepositions after verbs don't mark direct objects. And without a direct object, Passive is impossible.
The real solution is to get a new textbook that actually describes English, instead of something like English.
Without going into grammatical issues such as what "known" is, whether it is in the passive voice or not, whether it is a verb or an adjective, and such, and without caring about the risk of information loss or change due to the difference in information delivery, which is the whole point of the passive voice, you can rewrite the sentence with know like this:
The individual is rarely brought into the spotlight in a country that/which people/we know for its collective thought.
(You may also find this good answer on relative clauses and pied-piping useful.)
Best Answer
It is grammatical, but in this context it sounds unnatural and does in fact change the meaning. A more natural sounding version would be along the lines of