Coins in equilateral lattice

$n(n+1)/2$ coins are placed on an equilateral lattice with side $n$, such that all but one coin are showing heads.

At each step, one is allowed to choose two adjacent coins $A$ and $B$, and then flip all coins on the line $AB$ (and its extension).

Characterize all starting configuration such that it's always possible to get all tails.