For \( t \in (0, 2\pi) \), if \( ABC \) is an equilateral triangle with vertices \( A(\sin t, -\cos t) \), \( B(\cos t, \sin t) \) and \( C(a, b) \) such that its orthocenter lies on a circle with centre \( \left(1, \dfrac{1}{3}\right) \), then \( (a^2 - b^2) \) is equal to:
