For a triangle $\Delta$, let its pedal triangle be $P_1$ and let $P_n$’s pedal triangle be $P_{n+1}$.

Call $\Delta$ “P-Similar” if even any one of $P_1, P_2, P_3, P_4, P_5, P_6, P_7, P_8, \ldots$ is similar to $\Delta$.

How many trios of $(a, b, c)$ exist for $(a, b, c)$ being integers and $a \leq b \leq c$ such that a triangle with angles $a, b, c$ is “P-Similar”?

Angles are measured in degrees.

For clarification, Pedal Triangle here refers to the Orthic-Pedal triangle.