A flat rectangular plate with dimensions \(0.40 \text{ m} \times 0.50 \text{ m}\) is placed in a region of uniform electric field \(\vec{E} = (300\,\hat{\text{i}} - 300\,\hat{\text{j}} - 300\,\hat{\text{k}}) \text{ N/C}\). The orientation of the plate is defined by the unit normal vector \(\hat{n} = \dfrac{2}{3}\,\hat{\text{i}} - \dfrac{2}{3}\,\hat{\text{j}} + \dfrac{1}{3}\,\hat{\text{k}}\). What is the electric flux through the plate?