Vinogradov's theorem with almost equal summands

Let θ>11/20θ>11/20. We prove that every sufficiently large odd integer nn can be written as a sum of three primes n=p1+p2+p3n=p1+p2+p3 with |pi−n/3|⩽nθ|pi−n/3|⩽nθ for i∈{1,2,3}i∈{1,2,3}.