Let $C_\lambda$ the cantor set which is defined by the IFS $\{\lambda x,\lambda x+(1-\lambda)\}$ and also let $E=C_\lambda\times C_\lambda$.Suppose $\lambda =\frac 1 3$, we get the standard middle-thirds cantor sets. Denote the orthogonal projection of the set from the plane to the line which makes $\theta$ degrees. show that $P_\theta E$ contains an interval for a.e $\theta$.
Here I don't know from where to start. I know that the Lebesgue measure of the set is non-negative but that's not really useful here. I'll be glad for any hint.