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We study the tomographic clustering properties of the photometric cluster catalogue derived from the third data release of the Kilo Degree Survey (KiDS), focusing on the angular correlation function and its spherical harmonic counterpart: the angular power spectrum. We measured the angular correlation function and power spectrum from a sample of 5162 clusters, with an intrinsic richness of λ* ≥ 15, in the photometric redshift range of z ∈ [0.1, 0.6]. We compared our measurements with theoretical models, within the framework of the Λ cold dark matter cosmology. We performed a Markov chain Monte Carlo (MCMC) analysis to constrain the cosmological parameters, Ωm and σ8, as well as the structure growth parameter, S8 ≡ σ8√Ωm/0.3. We adopted Gaussian priors on the parameters of the mass-richness relation, based on the posterior distributions derived from a previous joint analysis of cluster counts and weak-lensing mass measurements carried out on the basis of the same catalogue. From the angular correlation function, we obtained Ωm = 0.32−0.04+0.05, σ8 = 0.77−0.09+0.13, and S8 = 0.80−0.06+0.08, which are in agreement, within 1σ, with the 3D clustering result based on the same cluster sample and with existing complementary studies on other data sets. For the angular power spectrum, we checked the validity of the Poissonian shot noise approximation, also considering the mode-mode coupling induced by the mask. We derived statistically consistent results, in particular, Ωm = 0.24−0.04+0.05 and S8 = 0.93−0.12+0.11; while the constraint on σ8 alone is weaker with respect to the one provided by the angular correlation function, σ8 = 1.01−0.17+0.25. Our results show that the 2D clustering from photometric cluster surveys can provide competitive cosmological constraints with respect to the full 3D clustering statistics. We also demonstrate that they can be successfully applied to ongoing and forthcoming spectrometric and photometric surveys. [ABSTRACT FROM AUTHOR]