An eigenfuntion expansion method is employed for obtaining three-dimensional asymptotic displacement and stress fields in the vicinity of the front of a crack/anticrack type discontinuity weakening/reinforcing an infinite pie-shaped trimaterial plate, of finite thickness, formed as a result of bimaterial (matrix/semiconductor/ARC plus reaction product/scatterer) deposit over a substrate (fiber/ARC/semiconductor). The wedge is of general (unsymmetric) geometrical configuration, and is subjected to antiplane shear (mode III) far field loading. Each material is isotropic and elastic, but with different material properties. The material 2 or the substrate is always taken to be a half-space, while the wedge aperture angle of the material 1 is varied to represent varying composition of the bimaterial deposit. Numerical results pertaining to the variation of the mode III eigenvalues (or stress singularities) with various wedge aperture angles of the material 1 (reaction product/scatterer), are also presented. Hitherto generally unavailable results, pertaining to the through-thickness variations of stress intensity factors for symmetric parabolic load and its skew-symmetric counterpart that also satisfy the boundary conditions on the top and bottom surfaces of the trimaterial plates under investigation, form also an important part of the present investigation.