  The transverse momentum distribution of the $t\bar{t}$ system is of both
experimental and theoretical interest. In the presence of the azimuthally
asymmetric divergences, pursuing the resummation at the high logarithmic
precision is rather demanding in general. In this paper, we propose the
projected transverse momentum spectrum $\mathrm{d}\sigma_{t\bar{t}}/\mathrm{d}
q_{\tau}$, which is derived from the classical $\vec{q}_{\mathrm{T}}$ spectrum
by integrating out the rejection component $q_{\tau_{\perp}}$ with respect to a
reference unit vector $\vec{\tau}$, to serve as an alternative resolution to
curb those asymmetric influences, in additional to the azimuthally averaged
case $\mathrm{d}\sigma_{t\bar{t}}/\mathrm{d} |\vec{q}_{\mathrm{T}}|$. In the
context of the effective field theories, SCET$_{\mathrm{II}}$ and HQET, we will
demonstrate that in spite of the $q_{\tau_{\perp}}$ integrations, the leading
asymptotic terms of $\mathrm{d}\sigma_{t\bar{t}}/\mathrm{d} q_{\tau}$ still
observe the factorization pattern in terms of the hard, beam, and soft
functions in the vicinity of $ q_{\tau}=0$~GeV. With the help of the
renormalisation group equation techniques, we evaluate the resummed spectra
$\mathrm{d}\sigma_{t\bar{t}}/\mathrm{d} q_{\mathrm{T,in}}$,
$\mathrm{d}\sigma_{t\bar{t}}/\mathrm{d} q_{\mathrm{T,out}}$, and
$\mathrm{d}\sigma_{t\bar{t}}/\mathrm{d} \Delta\Phi_{t\bar{t}}$ at NLL+NLO,
NNLL+NNLO, and approximate NNLL'+NNLO accuracy. This is the first time the
azimuthal spectrum $\Delta\Phi_{t\bar{t}}$ is appraised at or beyond the NNLL
level including a consistent treatment of both beam collinear and soft
radiation.
