Equations on Integration!

Calculus Level 5

$\large{\int_0^x tf(x-t)\ \mathrm{d}t = \int_0^x f(t)\ \mathrm{d}t + \sin(x) + \cos(x) -x-1}$

Find a continuous function $$f(x)$$ such that for all real $$x$$, the above equation is satisfied. Determine the value of $$f \left( \frac{\pi}6 \right)$$ to three decimal places.

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