Let \( PQ \) be a focal chord of the parabola \( y^2 = 4x \) such that it subtends an angle of \( \pi/2 \) at the point \( (3, 0) \). Let the line segment \( PQ \) be also a focal chord of the ellipse \( E : \, \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \, a^2 > b^2 \). If \( e \) is the eccentricity of the ellipse \( E \), then the value of \( \frac{1}{e^2} \) is equal to:
