\(x-y=\dfrac{\Omega}{3}\)
=>\(x=y+\dfrac{\Omega}{3}\)
\(A=\left(cosx+cosy\right)^2+\left(sinx+siny\right)^2\)
\(=cos^2x+cos^2y+2\cdot cosx\cdot cosy+sin^2x+sin^2y+2\cdot sinx\cdot siny\)
\(=2\cdot cosx\cdot cosy+2\cdot sinx\cdot siny+2\)
\(=2\cdot cosy\cdot cos\left(y+\dfrac{\Omega}{3}\right)+2\cdot siny\cdot sin\left(y+\dfrac{\Omega}{3}\right)+2\)
\(=2\cdot cosy\cdot\left[cosy\cdot cos\left(\dfrac{\Omega}{3}\right)-siny\cdot sin\left(\dfrac{\Omega}{3}\right)\right]+2\cdot siny\cdot\left[siny\cdot cos\left(\dfrac{\Omega}{3}\right)-cosy\cdot sin\left(\dfrac{\Omega}{3}\right)\right]+2\)
\(=2cosy\left[cosy\cdot\dfrac{1}{2}-siny\cdot\dfrac{\sqrt{3}}{2}\right]+2\cdot siny\cdot\left[\dfrac{1}{2}siny-\dfrac{\sqrt{3}}{2}\cdot cosy\right]+2\)
\(=cos^2y-\sqrt{3}\cdot cosy\cdot siny+sin^2y-\sqrt{3}\cdot siny\cdot cosy+2\)
\(=\left(cos^2y+sin^2y\right)-2\sqrt{3}\cdot siny\cdot cosy+2\)
\(=1-\sqrt{3}\cdot sin2y+2=3-\sqrt{3}\cdot sin2y\)
