There are a number of reasons why Turkey invaded Cyprus.
1. The coup d'état was seen as a threat to Turkey's security. Turkey had long been concerned about the possibility of Cyprus becoming a base for Greek military operations, which could threaten Turkey's southern coast. The coup increased these fears, as the new Greek Cypriot government was seen as more closely aligned with Greece.
2. Turkey was concerned about the safety of the Turkish Cypriot minority in Cyprus. The Turkish Cypriots make up about 18% of the population of Cyprus, and they have long been a marginalized minority. The coup, which was supported by many Greek Cypriots, led to increased violence against Turkish Cypriots, and Turkey feared that the Turkish Cypriots would be harmed if the coup were successful.
3. Turkey wanted to protect its economic interests in Cyprus. Turkey had significant economic interests in Cyprus, including a number of businesses and investments. The coup threatened these interests, as the new government was seen as less favorable to Turkey.
4. Turkey was concerned about the status of Cyprus under the 1960 constitution. The 1960 constitution had established Cyprus as a bi-communal state, with power shared between the Greek Cypriot majority and the Turkish Cypriot minority. The coup threatened this arrangement, as the new Greek Cypriot government was seen as undermining the rights of the Turkish Cypriots.
5. Turkey wanted to assert its dominance in the Eastern Mediterranean. Turkey is a regional power, and it has long sought to assert its dominance in the Eastern Mediterranean. The invasion of Cyprus was seen as a way to demonstrate Turkey's power and to increase its influence in the region.