Let g be a differentiable function such that $\int_0^x g (t)dt = x - \int_0^x t g(t)dt,x \ge 0$ and let $y = y(x)$ satisfy the differential equation $\frac{{dy}}{{dx}} - y\tan x = 2(x + 1)\sec xg(x),x \in \left[ {0,\frac{\pi }{2}} \right)$. If $y(0) = 0$, then $y\left( {\frac{\pi }{3}} \right)$ is equal to