You got a good case with pi/2, it's truly useful, as it represents the angle between 3d axes, the boundaries of the tangent and inverse trigonometric functions, the monotonic regions of cosine and sine etc. It will even make spherical coordinates easier to visualize mentally. (It will also make a two-digit number, 16, a common resident in lots of formulas). I vouch for it, and i call for a move to name it, confusingly, pi-bar