2. The Angle of Deviation. When a light ray hits a raindrop, the light undergoes a sequence of reflections inside the water droplet. The total rotation that the light ray undergoes is given by D(x)= *+2x -4sin - sin(x) k The input x measures the angle (in radians) that the light ray forms with the surface of the spherical raindrop so the domain of D is 0, 7]. The output, D(x), is also an angle in radians. The constant k 21 is called the index of refraction and depends on the color of the light. Find the minimum value of D when k=$5/2. Using trig identities, it is possible to write your answer in the formarccos(r ) for some rational number r. Your solution should show the derivative, your calculation of the critical number, and the final maximum value in the form arccos(r)