Integral Equation and Function Analysis

Let f be a twice differentiable function such that $f(x)=\int\limits_{0}^{x} \tan(t-x) dt - \int\limits_{0}^{x} f(t) \tan t dt, \quad x \in \left( -\dfrac{\pi}{2}, \dfrac{\pi}{2} \right)$ Then $f''\;\left( \dfrac{\pi}{6} \right) + 12 f'\;\left( -\dfrac{\pi}{6} \right) + f\;\left( \dfrac{\pi}{6} \right)$ is equal to ____ .