For what its worth and even if this is not an Excel forum: here a sheet, zipped.
The sheet contains a function "KeplerZero" which solve the equation F(x,c) = x - c*sin(x) = 0 for a given c, 1 < c, 0 < x < Pi.
At the boundaries one can use a Taylor series for F, it is alternating and therefore that approximation error can be estimated.
In x = 0 one takes series = polynom of degree 5, and the task easily reduced to solve a quadratic equation.
In x = Pi one takes degree 3, a depressed cubic with 3 real roots (Descartes rule of sign).
Between those ranges one uses a root finder, already a bisection method will do
Note: for increasing c the task runs into catastrophic cancellations since both summands are necessarily of same size
and achieving zero means that their leading digits have to cancel out. Meaning that the true value can not be seen.
PS: one can use it with Open Office / Libre Office as well, the code should work.
axelvogt.de/temp/KeplerZero_BiSection.xls (I can not upload it here ...)