Difficult Mechanics 2 Problem

A uniform Lamina is in the shape of an Equilateral triangle ABC, and rest in equilibrium inside a vertical hoop with B and C in contact with the hoop, and A at the center of the circle. Contact is smooth at C but rough at B, where the coefficient of friction is U (mu). The lamina is in limiting equilibrium with B lower than C, and the axis of symmetry through A makes an angle theta with the vertical. By first taking moments about A show that tan(theta)=U*sqrt(3)/sqrt(3)-U

What have you tried??

A uniform Lamina is in the shape of an Equilateral triangle ABC, and rests in equilibrium inside a vertical hoop with B and C in contact with the hoop, and A at the center of the circle. Contact is smooth at C but rough at B, where the coefficient of friction is U (mu). The lamina is in limiting equilibrium with B lower than C, and the axis of symmetry through A makes an angle theta with the vertical. By first taking moments about A show that $\tan\theta$=U*$\sqrt3$/($\sqrt3$-U)

Having spent several hours trying to do it via the suggested method and getting it wrong, I resorted to triangle of forces (combined the forces at B into one to reduce the count to three).

And get $\displaystyle \tan \theta = \frac{\sqrt{3}\mu}{\sqrt{3}-2\mu}$

Which although different to the desired result in your first post, does agree with a thread on stackexchange. And the working was a hell of a lot simpler.