This paper establishes a rigorous real-analytic and geometric framework governing the distribution of the non-trivial zeros of the Dirichlet eta function $eta(s)$ across the critical strip $mathcal{S} = {s in mathbb{C} : 0 < Re(s) < 1}$. Diverging from traditional statistical and global zero-density bounds, we introduce a localized, deterministic algebraic mechanism defined as textit{Trigonometric Annihilation}. By decomposing $eta(s)$ into its strictly positive, monotonic real-axis baseline profile $eta(sigma)$ and two conditionally convergent, alternating quadratic half-angle residual series, we demonstrate that the vanishing of the real part at any exact root mathematically forces the underlying sine and cosine summation values into absolute scalar parity. This dual equilibrium inherently triggers the universal Pythagorean identity ($sin^2 theta + cos^2 theta = 1$) across the conditionally convergent series, entirely neutralizing the highly oscillatory complex frequency variable $t_0$. The most profound consequence of this annihilation is the textit{monotonic transformation} of the dynamic differences. Deprived of all dynamic oscillatory elasticity, the residual series irreversibly freeze onto the static real baseline. Consequently, the highly malleable dynamic differences $Delta S_{mathrm{Re}}$ and $Delta S_{mathrm{Im}}$ are structurally forced to inherit the strict monotonicity of the static disparity function $A(sigma) = eta(sigma) - eta(1-sigma)$. Under functional reflection symmetry, any hypothetical off-line zero must simultaneously satisfy $A(sigma_0) = Delta S_{mathrm{Re}} = Delta S_{mathrm{Im}}$. However, because Trigonometric Annihilation forces the $Delta S$ parameters to become strictly monotonic, they absolutely lose the geometric elasticity required to bridge the expanding static gap $A(sigma) eq 0$. Furthermore, to definitively resolve the Davenport-Heilbronn obstruction, we directly link this geometric rigidity to the arithmetic distribution of primes via the Euler product and the von Mangoldt function. This absolute monotonic constraint dictates that the dynamically frozen series can only satisfy the functional reflection condition if they simultaneously vanish at the unique geometric origin ($A=0$). Thus, the existence of non-trivial zeros off the critical line is reduced from a probabilistic density inquiry to a deterministic structural contradiction, unconditionally confining all non-trivial zeros to the critical line $Re(s) = 1/2$.