The state that was established by the Constitution (36th Amendment) Act, 1975 is Sikkim.

Explanation:
Sikkim, a small landlocked state in northeastern India, became the 22nd state of the Indian Union on May 16, 1975, after the Constitution (36th Amendment) Act was passed. The Act amended the First Schedule of the Indian Constitution, which lists the names of the states and union territories of India.

Sikkim was a protectorate of India from 1950 until 1975. It had its own monarch and administration, but India was responsible for its defense, foreign affairs, and communication. In the early 1970s, Sikkim witnessed political turmoil and protests against the monarchy. There were demands for greater democracy and integration with India.

Key Points:
- The Constitution (36th Amendment) Act, 1975 was enacted to address the demands for integration and democracy in Sikkim.
- The Act amended the First Schedule of the Indian Constitution to include Sikkim as a state of India.
- This meant that Sikkim would no longer be a protectorate but would have full statehood within the Indian Union.
- The amendment also repealed the provisions of the Sikkim Constitution that related to the monarchy and established a democratic system of government.
- After the amendment, Sikkim adopted a parliamentary form of government with a Chief Minister and a Council of Ministers.
- The monarchy was abolished, and Sikkim became a constitutional monarchy with the Chogyal (King) as the ceremonial head of state.
- The amendment also provided for the integration of Sikkim's legislature with the Indian Parliament. Sikkim was allocated one seat in the Lok Sabha (the lower house of Parliament) and one seat in the Rajya Sabha (the upper house).
- The Constitution (36th Amendment) Act, 1975 was a significant step in the process of Sikkim's integration into the Indian Union and the establishment of democratic governance in the state.

In conclusion, the Constitution (36th Amendment) Act, 1975 established Sikkim as a state of India, ending its status as a protectorate and granting it full statehood within the Indian Union.