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The function solve aims at finding solutions symbolically, and it seems that Sage is not able to do it for your equation. If you want to solve your equation numerically, you can use find_root as follows:

sage: find_root(1/3*x + sin(2*x)-1,0,1)
0.49428348982550824
sage: find_root(1/3*x + sin(2*x)-1,1,2)
1.261800196654962

The function solve aims at finding solutions symbolically, and it seems that Sage is not able to do it for your equation. If you want to solve your equation numerically, you can use find_root as follows:

sage: find_root(1/3*x + sin(2*x)-1,0,1)
sin(2*x) - 1, 0, 1)
0.49428348982550824
sage: find_root(1/3*x + sin(2*x)-1,1,2)
sin(2*x) - 1, 1, 2)
1.261800196654962

The function solvesolve() aims at finding solutions symbolically, and it seems that Sage is not able to do it for your equation. If you want to solve your equation numerically, you can use the function find_rootfind_root() as follows:

sage: find_root(1/3*x + sin(2*x) - 1, 0, 1)
0.49428348982550824
sage: find_root(1/3*x + sin(2*x) - 1, 1, 2)
1.261800196654962