aṅgiras, marīci, atri, vasiṣṭha, pulaha, pulastya, kratu are the mānasaputras of brahma. The geneology of vasiṣṭha is like this:
marīci > kaśyapa > mitra varuṇa > vasiṣṭha > 1. indrapramadi, 2. śakti, 3. maitrāvaruṇa
1. indrapramadi > ābharadvasu > upamanyu
2. śakti > parāśara
3. maitrāvaruṇa > kuṇḍita
If we look at kaśyapa vamśāvali, it shows the following:
marīci > kaśyapa > 1. avatsāra, 2. asita
1. avatsāra > 1a. rebha, 1b. nidruva
2. asita > devala
agastya vaṃśa is :-
kaśyapa > mitrāvaruṇa > agastya > dṛḍhacyuta > idhmavāha
Thus we find that agastya and vasiṣṭha are patrilineal, actually brothers.
viṣṇuvṛddha and harīta gotras also trace back to marīci: marīci > kaśyapa >vivasvān > manu > ikṣvāku ...>yuvanāśva > mandhātā > 1. purukutsa, 2. ambarīṣa
1. purukutsa > trasadasyu > sambhūta > viṣṇuvṛddha
2. ambarīṣa > yuvanāśva > harīta
Now let us see how the pravaras (rishi lineages to be recited in the abhivādaye), gotras and sūtras are all mixed up.
āṅgirasa - ājamīḍa - kāṇva — ājamīḍa gotra — āpastamba sūtra
āṅgirasa - ājamīḍa - kāṇva — gardabha gotra — matsya sūtra
āṅgirasa - kaurava - kāṇva — gardabha gotra — āśvalāyana sūtra
āṅgirasa - gauruvīta - sāṅkṛtya — cāndrāyaṇa gotra — bodhāyana sūtra
sādhya - sāṅkṛtya - gauruvīta — saṃkṛti gotra — āpastamba sūtra
vaiśvāmitra - daivarāta - audala — jābāla gotra — bodhāyana / kātyāyana / laugākṣi gotras
vaiśvāmitra - daivarāta - audala — devarāta gotra — āpastamba sūtra
It will thus be seen that if we have to go by "unrelated" gotras in the patrilineal sense of the term, many gotras would have to be discarded. It is my considered view that the gotras or tribal groups which got absorbed into the Aryan way of living and were granted brahman status, were also bestowed with a certain gotra and a suitable lineage from one of the well-known rishis. That is how we get different gotras for father, son, grandson etc.
Note: Details re. lineages, gotra, pravara, sutra, etc., taken from the book "rishikalum gotrangalum", Lifco publication, 1974.