  In this work, we systematically study two phases, called Andreev $\pi$-phase
and orbital-phase, and their influence on the Josephson effect. When the system
is time-reversal invariant and centrosymmetric, these two phases only appear in
the odd-parity pairings. The Andreev $\pi$-phase has nothing to do with the
specific form of the odd-parity pairings and means an intrinsic $\pi$-phase
between the spin-triplet Cooper pairs entering and leaving CTSCs in the Andreev
reflections. The orbital-phase corresponds to the phase difference between the
spin-triplet Cooper pairs with opposite spin polarization and depends on the
specific form of the odd-parity gap functions. When the normal region of the
Josephson junction contacts the same side of the CTSCs with some specific
odd-parity parings, the competition between the two phases can lead to the
Josephson $\pi$-junction. Note that this junction is different from that of the
conventional Josephson junction (JJ) and is dubbed a U-shaped junction
according to its geometry. Meanwhile, in a conventional JJ, the interplay of
these two phases causes their impact on the CPR to be completely canceled out.
Therefore no matter what kind of pairing symmetries the CTSC has, it will lead
to Josephson 0-junction in this case. We obtain our results based on the model
of the M$_{x}$Bi$_2$Se$_3$ family where M may be Cu, Sr, or Nb. Therefore, we
propose to detect the pairing symmetry of M$_{x}$Bi$_2$Se$_3$ through a
superconducting quantum interference device containing a U-shaped Josephson
junction.
