This question is from Mechanics, not NLM. Torque about point A should be zero since the body is in rotational equilibrium. For this condition, the weight of the body must pass through point A, or else it will produce a non zero torque about A which is not possible.
the weight of the body must pass through point A
For this, the centre of mass of the body should lie below point A.
On solving this, we get tanθ = 1/3