Given that

\(y=\ln(1+\sin x),\qquad 0\lt x\lt\pi,\)

(a) find \(\dfrac{dy}{dx}\),

(b) find the exact value of \(\dfrac{dy}{dx}\) when \(x=\dfrac{\pi}{6}\), giving your answer in the form \(\dfrac1{\sqrt a}\), where \(a\) is an integer,

(c) solve the equation \(\dfrac{dy}{dx}=\tan x\).