We report the first ground-based transit observation of K2-3d, a 1.5 R_Earth planet supposedly within the habitable zone around a bright M-dwarf host star, using the Okayama 188 cm telescope and the multi(grz)-band imager MuSCAT. Although the depth of the transit (0.7 mmag) is smaller than the photometric precisions (1.2, 0.9, and 1.2 mmag per 60 s for the g, r, and z bands, respectively), we marginally but consistently identify the transit signal in all three bands, by taking advantage of the transit parameters from K2, and by introducing a novel technique that leverages multi-band information to reduce the systematics caused by second-order extinction. We also revisit previously analyzed Spitzer transit observations of K2-3d to investigate the possibility of systematic offsets in transit timing, and find that all the timing data can be explained well by a linear ephemeris. We revise the orbital period of K2-3d to be 44.55612 pm 0.00021 days, which corrects the predicted transit times for 2019, i.e., the era of the James Webb Space Telescope, by sim80 minutes. Our observation demonstrates that (1) even ground-based, 2 m class telescopes can play an important role in refining the transit ephemeris of small-sized, long-period planets, and that (2) a multi-band imager is useful to reduce the systematics of atmospheric origin, in particular for bluer bands and for observations conducted at low-altitude observatories.
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