Talk:2011 AMC 12B Problems/Problem 10

Let θ = AMD and let MCD = x. We can see that AMCD is a right trapezoid, so 2θ + 90 + 90 + x = 360. This means that x = 180 - 2θ. We can solve for MD by acknowledging AMD as a right triangle. This means cos(θ) = 3/MD, so MD = 3/cos(θ). Now using triangle MCD, using law of sines, we can figure out that 6/sinθ=(3/sinθ)/sin2θ. We cancel out sinθ and are left with 6 = 3/sin2θ. Now it is clear that sin2θ = 1/2, so 2θ= 30 and θ = 15. But 15 isn't our answer according to online resources. What did I do wrong???