coordinate - Declination change due to precession

I'm not absolutely sure if it is correct, but I use information from this site: http://star-www.st-and.ac.uk/~fv/webnotes/chapt9a.htm

And I convert equatorial coordinates (RA = α, Dec = δ) to ecliptic coordinates (λ, β) using this formula.

sin(β) = sin(δ) cos(ε) - cos(δ) sin(ε) sin(α)

cos(λ) cos(β) = cos(α) cos(δ)

ε = Axial tilt (23,5°)

I know that due to precession only λ changes (β remains same for ecliptic coordinates). So I add the angle of precession to the λ. Then I convert the new λ and β back to the equatorial coordinates.

sin(δ) = sin(β) cos(ε) + cos(β) sin(ε) sin(λ)

cos(λ) cos(β) = cos(α) cos(δ)