The smallest positive value

Find the smallest positive value of $x$ in radians such that the smallest positive value of $\sin(x)+\cos(x)+\tan(x)+\cot(x)+\csc(x)+\sec(x)$ is attained.

Choose the value of $\frac{\pi}{\text{hi}}$ , where $\text{hi}$ is the required value of $x$ .

Inspired by this .