At \(700\text{ K}\), the equilibrium constants for two gas-phase reactions are given below:

\[ 2\,\text{NO}_2\text{(g)} \rightleftharpoons 2\,\text{NO(g)} + \text{O}_2\text{(g)} \quad\quad K_1 = 3.6 \times 10^{-2} \]

\[ \text{N}_2\text{(g)} + \text{O}_2\text{(g)} \rightleftharpoons 2\,\text{NO(g)} \quad\quad K_2 = 4.0 \times 10^{-5} \]

Based on these data, what is the value of the equilibrium constant, \(K_3\), at \(700\text{ K}\) for the reaction represented below?

\[ \text{NO}_2\text{(g)} \rightleftharpoons \frac{1}{2}\,\text{N}_2\text{(g)} + \text{O}_2\text{(g)} \quad\quad K_3 = \,? \]