If the equation of the pair of straight lines passing through the point (1,1) one making an angle θ with the positive direction of the x-axis and the other making the same angle with the positive direction of the y-axis, is x2−(a+2)xy+y2+a(x+y−1)=0,a≠−2,then the value of sin2θ is

The equations of the given lines are y−1=tan θ (x−1) and y−1=cot θ (x−1)So, their joint equation is [(y−1)−tan θ (x−1)][y−1−cot θ (x−1)]=0 or (y−1)2−(tanθ+cot θ) (x−1)(y−1)+(x−1)2=0or x2−(tanθ+cot θ)xy+y2+(tan θ+cot θ−2)(x+y−1)=0Comparing with the given equation, we get tanθ+cot θ=a+2 or 1sin θ cosθ=a+2 or sin 2θ =2a+2