We calculate various azimuthal angle distributions for three jets produced in the forward rapidity region with transverse momenta p(T) > 20 GeV in proton-proton (p-p) and proton-lead (p-Pb) collisions at center of mass energy 5.02 TeV. We use the multiparton extension of the so-called small-x Improved Transverse Momentum Dependent factorization (ITMD). We study effects related to change from the standard k(T)-factorization to ITMD factorization as well as changes as one goes from p-p collision to p-Pb. We observe rather large differences in the distribution when we change the factorization approach, which allows to both improve the small-x TMD gluon distributions as well as validate and improve the factorization approach. We also see significant depletion of the nuclear modification ratio, indicating a possibility of searches for saturation effects using trijet final states in a more exclusive way than for dijets.