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sage: solve(sin(x)+cos(x)==2,x,to_poly_solve=True)
[x == 1/4*pi + 2*pi*z6 - I*log(-1/2*(sqrt(2) - 2)*sqrt(2)), x == 1/4*pi + 2*pi*z8 - I*log(sqrt(2) + 1)]

Note that one gets a family of solutions because these are multi-valued inverses.

The to_poly_solve option still is not documented in the global solve?, but will show up if you do x.solve?. Apologies for not having done this.