I just figured it out and its hard than I thought it would be.
The trick is that you need to find the centripetal force. This is the total force acting directly towards the centre (not down the slope).
To do this, you need to find the component of the frictional force that is acting centripetally. The frictional force does give a centripetal force equal to the weight because its not acting exactly towards the middle.
Also, the mg sin(20) term that you added to the centripetal force is incorrect. This would be correct in a situation with no friction, but adding friction makes it more complicated. The friction is acting down the slope, so you need to consider the normal force. The vertical component of the normal force will cancel out with the vertical component of the friction, and the weight. You then need to find the component of the normal force which is acting centripetally.