When high$-$energy charged particles move through a transparent medium with a speed greater than the speed of light in that medium, a shock wave, or bow wave, of light is produced. This phenomenon is called the Cerenkov effect. When a nuclear reactor is shielded by a large pool of water, Cerenkov radiation can be seen as a blue glow in the vicinity of the reactor core due to high$-$speed electrons moving through the water. In a particular case, the Cerenkov radiation produces a wave front with an apex half$-$angle of $56\mathrm{.}0.$ Calculate the speed of the electrons in the water. The speed of light in water is $2\mathrm{.}25108$ m$/$s$.$

m$/$s