To find the solutions to the equation given, we set each factor to 0 and solve for x.

First factor: sinx - 1/2 = 0
sinx = 1/2
This happens when x = π/6 or x = 5π/6.

Second factor: 2cosx - 1 = 0
cosx = 1/2
This happens when x = π/3 or x = 5π/3.

Third factor: tgx - 1 = 0
tanx = 1
This happens when x = π/4.

Therefore, the solutions to the equation (sinx - 1/2) (2cosx - 1) (tgx -1) = 0 are x = π/6, 5π/6, π/3, 5π/3, and π/4.