Finding languages such that $L_1\subset L_2\subset L_3$ where $L_1,L_3\notin$ RE and $L_2\in$ R

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I am struggling to find such languages $L_1$, $L_2$, and $L_3$ such that $L_1\subset L_2\subset L_3$ where $L_1,L_3\notin$ RE and $L_2\in$ R.

I know they exist, I need help finding them.

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Let $L$ be some language not in RE. Take

  • $L_1 = 0L$.
  • $L_2 = 0\Sigma^*$.
  • $L_3 = 0\Sigma^* \cup 1L$.