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We discuss detectability of the nonlinear growth of the large-scale structure in the cosmic microwave background (CMB) lensing. Lensing signals involved in CMB anisotropies have been measured from multiple CMB experiments, such as Atacama Cosmology Telescope (ACT), Planck, POLARBEAR, and South Pole Telescope (SPT). Reconstructed lensing signals are useful to constrain cosmology via their angular power spectrum, while detectability and cosmological application of their bispectrum induced by the nonlinear evolution are not well studied. Extending the analytic estimate of the galaxy lensing bispectrum presented in Takada and Jain (2004) to the CMB case, we show that even near term CMB experiments such as Advanced ACT, Simons Array and SPT3G could detect the CMB lensing bispectrum induced by the nonlinear growth of the large-scale structure. In the case of the CMB Stage-IV, we find that the lensing bispectrum is detectable at $\gtrsim 50\,\sigma$ statistical significance. This precisely measured lensing bispectrum has rich cosmological information, and could be used to constrain cosmology, e.g., the sum of the neutrino masses and the dark-energy properties.