State the Dahlquist equivalence theorem regarding convergence of a multistep method.

The multistep method, with a real parameter $a$,

$$y_{n+3}+(2 a-3)\left(y_{n+2}-y_{n+1}\right)-y_{n}=h a\left(f_{n+2}-f_{n+1}\right)$$

is of order 2 for any $a$, and also of order 3 for $a=6$. Determine all values of $a$ for which the method is convergent, and find the order of convergence.