Let 𝑓:ℝ→ℝ be a differentiable function such that its derivative 𝑓′ is continuous and ƒ(𝜋) = −6.
If $F:[0, \pi] \rightarrow \mathbb{R}$ is defined by $F(x)=\int_0^{\mathrm{x}} f(\mathrm{t}) \mathrm{dt}$, and if
$ \int_0^\pi\left(f^{\prime}(\mathrm{x})+\mathrm{F}(\mathrm{x})\right) \cos \mathrm{x} \mathrm{dx}=2 $
then the value of $f(0)$ is $\_\_\_\_$