I already included the correct answer but can you please explain step by step how that was obtained?

Please kindly type the answer, I have hard time reading the handwritten. Thanks so much for your help. I appreciate it. My main question is about the T1 and T2. Are they output or T Flip flop or what? how did they get the table as well.

Design a sequential circuit that detects three consecutive 1's using T flip flops. By detect 1 , I mean if three consecutive 1's arrive, it goes to a state where the output is 1 and stays there until it gets an input of 0 . T1=Q1Q0IN+Q1Q0IN+Q1Q0INT0=Q0IN+Q0IN+Q1Q0