Let f(t)=∫((1- sin ( log_e t))/(1- cos ( log_e t))) d t, t>1. If f(e^π / 2)=-e^π / 2 and f(e^π / 4)=α e^π / 4, then α equals

Let $\displaystyle f(t)=\int\left(\frac{1-\sin \left(\log _e t\right)}{1-\cos \left(\log _e t\right)}\right) d t, t>1$. If $\displaystyle f\left(e^{\pi / 2}\right)=-e^{\pi / 2}$ and $\displaystyle f\left(e^{\pi / 4}\right)=\alpha e^{\pi / 4}$, then $\displaystyle \alpha$ equals