2D &= x_1y + xy_1 \\
&= a \sin \alpha \ a \cos \alpha + a \left( \frac{1}{2} \cos \alpha - \frac{\sqrt{3}}{2} \sin \alpha \right) a \left( \frac{\sqrt{3}}{2} \cos \alpha + \frac{1}{2} \sin \alpha \right) \\
&= \cdots \\
&= a^2 \left( \frac{\sqrt{3}}{2} ({\cos}^2 \alpha - {\sin}^2 \alpha) + \frac{1}{2} \cos \alpha \sin \alpha \right)