Sandwiching Languages I am studying for my algorithms final and came across the following problem:

Find three languages $L_1 \subset L_2 \subset L_3$ over the same alphabet such that $L_2 \in P$ and $L_1,L_3$ are undecidable.

I am having trouble coming up with an example of three such languages. My first thought was to use a form of the halting problem for both $L_1$ and $L_3$ since that is pretty much the only undecidable language I know and am familiar with. I was thinking of perhaps coming up with something of the form 
\begin{align*}
L_1 &amp;= \{M \mid \text{$M$ is a Turing machine that starts with 00 and halts}\}\\
L_2 &amp;= \{M \mid \text{$M$ is a Turing machine that starts with a 00}\}\\
L_3 &amp;= ?
\end{align*}
but this doesn't seem to be working.  Any ideas are appreciated!
Hint: Your approach can be completed and you need to change only one word in the description of $L_1$ to get a description for $L_3$ that works.