(a)

(i) Write

\(6xy+3y+4x+2\)

in the form \((ax+b)(cy+d)\), where \(a,b,c\) and \(d\) are positive integers.

(ii) Hence solve the equation

\(6\sin\theta\cos\theta+3\cos\theta+4\sin\theta+2=0\)

for \(0^\circ\lt\theta\lt360^\circ\).

(b) Solve the equation

\(\frac12\operatorname{sec}\left(2\phi+\frac{\pi}{4}\right)=\frac1{\sqrt3}\)

for \(-\pi\lt\phi\lt\pi\), where \(\phi\) is in radians. Give your answers in terms of \(\pi\).