<image>(2014 Autumn·Shangcheng District School-Level Midterm Exam) As shown in the figure, for the cube ABCD-A₁B₁C₁D₁, consider the following four propositions:

① When point P moves along the line BC₁, the volume of the tetrahedron A-D₁PC remains unchanged;
② When point P moves along the line BC₁, the angle between line AP and plane ACD₁ remains unchanged;
③ When point P moves along the line BC₁, the dihedral angle P-AD₁C remains unchanged;
④ M is a point in the plane A₁B₁C₁D₁ equidistant from points D and C₁. The locus of point M is a line passing through point D₁.

The number of true propositions is ____.