R: Force data.table to compute all interactions

Here is a data.table:

dat = data.table(var1=rnorm(120), var2=rep(c('a','b','c'),40), var3=rep(c(1,2,3,2,1,2,1,2,2,3,1,2),10))

dat2 = dat[,list(resp = mean(var1)),by=list(var2, var3)]

In dat2, only existing interactions of dat$var2 et dat$var3 are present. How can I force dat2 to contain results for all 9 possible interactions (instead of the 7 rows of dat2) for var2 and var3? If there is no direct solutions with data.table, what is the easiest way to solve this issue?

table(dat$var2, dat$var3)

     1  2  3
  a 20 10 10
  b 20 20  0
  c  0 30 10

Of course, for the interactions where no data exist in dat, dat2 should contain NA in resp.