probability or statistics – How to find sum of squares of data from a multivariate (Dirichlet) distribution?

Let $X = Dirichlet(1,1,1)$ be a tri-variate random variable with Dirichlet distribution with parameters all equal to 1. I need to find what $X_1^2+X_2^2+X_3^2$ will be.

I did TransformedDistribution(x^2+y^2+z^2, {x,y,z}(Distributed)DirichletDistribution({1,1,1})), but it doesn’t seem to do anything. What might be the problem?