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I have to find when does the integral equation has solution. I tried reading some toturials but don't really know what to do since all of them are about solving, not finding when it has solution.

I think I should use Fredholm alternative for this but I'm not sure what steps to make.

Could please someone explain me what to do? I don't want the straight answer, I want to understand principle of solving such task, I'll be very thankfull for help.

$$ f(x) = \phi(x) + \lambda \int_0^{2\pi} sin(x+t) f(t) \mathrm{d} t $$

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