The question implies for Case: 2 and Case: 3. We need to say two takbeers following one after the another if we face a situation described in the question.
The first takbeer is the mandatory Farz takbeer known as Takbeer-e-Tahreema (takbeerat al-ehram تكبيرة الإحرام).
this one would be counted as the first one of the six Farz [mandatory acts] inside salat known as ARKAN
The following takbeer i,e the second takbeer would be counted as the regular takbeers that we say while we do any movement in salat.
For Case: 1 we just need to say only one takbeer and attened the salat.
Note: Masbuk means a person who is late to join the salat with the Imam and misses at least One rakaat.