We can use the trigonometric ratios to solve for the unknown sides and angle:
Since A = π/3, we know that the opposite side (a) is 6 and the adjacent side (b) is unknown.
sin(A) = opposite/hypotenuse
sin(π/3) = 6/c
√3/2 = 6/c
c = 12/√3 = 4√3
cos(A) = adjacent/hypotenuse
cos(π/3) = b/4√3
1/2 = b/4√3
b = 2√3
Finally, we can use the Pythagorean theorem to find the remaining side:
a^2 + b^2 = c^2
6^2 + (2√3)^2 = (4√3)^2
36 + 12 = 48
√48 = 4√3
Therefore, the unknown sides are b = 2√3 and c = 4√3, and the unknown angle is B = π/2 - π/3 = π/6.