Function of infinite sum

Question

If $f(x) = \displaystyle\sum_{n = 1}^{\infty} (-1)^nx(x-1)^n$, then what is $f\left(\dfrac\pi4\right)$?

I tried to reduce it to a predefined infinite series but I was unable to do so.

Answer 1

Hint

$$\sum_{n=1}^\infty (-1)^nx (x-1)^n=x\sum_{n=1}^\infty (-1)^n(x-1)^n=x\sum_{n=1}^\infty (1-x)^n$$ Let $a=(1-x)$ and then ???