Orthogonality & Least Squares · Superchallenge problem

Apply Gram–Schmidt (without normalizing) to $1, x, x^2, x^3$ in the space of polynomials with inner product $\langle f, g\rangle = \displaystyle\int_0^1 f(x)g(x)\,dx$. The fourth output is a monic cubic $q_3(x)$. Find its constant term $q_3(0)$.