Need a hint proving that integral converges

I am trying to prove that $$\int_0^{\pi/4} (\tan x)^{-\alpha} dx$$ is finite for $$0 < \alpha < 1$$, where the integral denotes the Lebesgue integral with the Lebesgue measure. I've decided wether it converges for all other values of $$\alpha\in\mathbb{R}$$, but am simply stuck with this one.

I've tried using monotone convergence to integrate over the closed interval from 1/n to pi/4, where I can use the Riemann integral, but I can't figure out how to find an anti-derivative for the function. I've also tried finding a larger, integrable function but without luck.

Any hints would be much appreciated.

What happens if $$\alpha=1$$. Is that function integrable?