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let's say you know the torque and the I, the moment of inertia. Then $$\alpha= \frac{\tau}{I}$$ as you say you need ti to integrate the velocity V to get the angle. $$\theta=\int_{0}^t Vdt=\int_{0}^t\alpha*t*dt$$ And the angle after T seconds is $$\theta=1/2\alpha*t^2$$
Please note that in all likelyhood, I am repeating the book text. If the coordinate system A ($Ax'y'z'$) translates parallel with a constant velocity and acceleration from the fixed system O($Oxyz$), then the following equations hold: $$r_{A|O} + r_{B|A} = r_{B|O}$$ where: $r_{A|O}$ is the position of A with respect to O (usually this is abbreviated to \$r_{...