a₁ a₂ a₃ a₄ are the roots of the roots of the equation sin(A + B) = ksin2a, no two of which differ by a multiple of 2π, then a₁ + a₂ + a₃ + a₄ is equal to?

Expand the LHS and solve for A and B so as to attain the RHS trigonometric ratio, which in this case is Sin2a.

4 values as multiples of an angle would fall in the range of 0,2π corresponding to the values of a1, a2......... Add them to get the final answer.