How to calculate declination of Moon?
The complexity of the formula depends on the precision you need.
We can make a crude approximation with two sine waves: one for the Moon's travel eastward around the ecliptic over a
tropical month

$$\delta_1 = 23.4^\circ \sin {2 \pi (u - 10.75) \over 27.32158}$$

and one for the Moon's travel north or south of the ecliptic over a
draconic month

$$\delta_2 = 5.1^\circ \sin {2 \pi (u - 20.15) \over 27.21222}$$

both modified as the Moon goes faster or slower over an anomalistic month

$$u = t - 0.48 \sin {2 \pi (t - 3.45) \over 27.55455}$$

where t is the number of days since 2000-01-01 12:00 TT (J2000.0).
Then

$$\delta = \delta_1 + \delta_2$$

is within 1&deg; of the Moon's geocentric declination most of the time.
For a topocentric declination, subtract
1&deg; sin (observer's geographic latitude).

If you need higher precision, see
van Flandern and Pulkkinen 1979
or Meeus 1999
for more complicated formulas.

Note: the u and t offsets above are near a 0&deg; longitude crossing, an ascending node, and an apogee in January 2000 but are tweaked to minimize RMS differences from JPL HORIZONS lunar positions for 2000-2018.