If the equation of the pair of straight lines passing through the point `(1,1)` , one making an angle `theta` with the positive direction of the x-axis and the other making the same angle with the positive direction of the y-axis, is `x^2-(a+2)x y+y^2+a(x+y-1)=0,a!=2,` then the value of `sin2theta` is
(a) `a-2` (b) `a+2` (c) `2/(a+2)` (d) `2/a`

Options

A. `a-2`
B. `a+2`
C. `2//(a+2)`
D. `2//a`

Explanation

To solve the problem, we need to find the value of \( \sin 2\theta \) given the equation of a pair of straight lines that pass through the point \( (1,1) \) and make an angle \( \theta \) with the positive x-axis and y-axis.

### Step-by-Step Solution:

1. **Understanding the Given Equation**:
The given equation is:
\[
x^2 - (a + 2)xy + y^2 + a(x + y - 1) = 0
...