Measure of angles in radians

We know that the sum of all angles in a triangle is $180th^\circ$, since an equilateral triangle has three equal angles what we must write is $60^\circ$. Let's now convert this into radians by means of the conversion factor that transforms from degrees to radians: $$60^\circ \cdot \dfrac{2\pi \ \mbox{radians}}{360^\circ}=\dfrac{60\cdot 2\pi}{360}\mbox{radians} = \dfrac{\pi}{3} \mbox{radians} $$

We know that a full rotation is $360^\circ$, therefore three full rotations will be $3 \cdot 360^\circ$ giving a total of $1080^\circ$. But, on the other hand, we also know that a full rotation corresponds to the total longitude of the circumference which, in this case, is $2\pi$. If there are three turns, there are $3 \cdot 2\pi$ which equals $6\pi$ radians. If we prefer to do it by means of a conversion factors then: $$1080^\circ \cdot \dfrac{2\pi \ \mbox{radians}}{360^\circ}=\dfrac{1080\cdot 2\pi}{360}\mbox{radians} = 6\pi \ \mbox{radians} $$