Solve the equation 2arccosx−arcsin(1−2x2)=0 for all real x.
(i) Remove the inverse functions by introducing suitable trigonometric substitutions and obtain an equation solely in x.
(ii) Reduce the result of part (i) to a polynomial equation and solve it.
(iii) Discuss the admissibility of each root with respect to the domains of the inverse functions used in the original equation.