Please answer the following questions?

4sin(x)sin(3x)sin(5x)

    = 2(cos(3x-x)-cos(3x+x))sin(5x)

    = 2cos(2x)sin(5x) - 2cos(4x)sin(5x)

    = (sin(5x+2x)+sin(5x-2x)) - (sin(5x+4x)+sin(5x-4x))

    = sin(7x) + sin(3x) - sin(9x) - sin(x)

    = -sin(x) + sin(3x) + sin(7x) - sin(9x)

sin(75°)sin(45°)

    = (cos(75°-45°) - cos(75°+45°))/2

    = (cos(30°) - cos(120°))/2

    = (√3/2 + 1/2)/2 = (√3+1)/4

∴ sin(75°) = [(√3+1)/4]/(√2/2)

      = (√3+1)/(2√2)

      = (√6+√2)/4 ≒ 0.965926