Prove $\ell(\theta^{(t+1)}) \geq \ell(\theta^{(t)})$, answer proof not clear, need some expainations

Question

Question

The problem is to proof the inequation, but the answer is too elliptical, can anyone give some comment or explaination to help me build up the logic chain?

Answer

The confusion part:

1. why (1) is not $=$.
2. (2) why they directly come up $\theta^{(t+1)} > \theta^{(t+1)}$.
3. is there missing something between (0) and (1)?