  We consider the variational principle in the covariant formulation of
modified teleparallel theories with second order field equations. We vary the
action with respect to the spin connection and obtain a consistency condition
relating the spin connection with the tetrad. We argue that since the spin
connection can be calculated using an additional reference tetrad, modified
teleparallel theories can be interpreted as effectively bigravity theories. We
conclude with discussion about the relation of our results and those obtained
in the usual, non-covariant, formulation of teleparallel theories and present
the solution to the problem of choosing the tetrad in $f(T)$ gravity theories.
