(a) Solve

\(\tan(\alpha+45^\circ)=-\frac1{\sqrt2}\)

for \(0^\circ\leq\alpha\leq360^\circ\).

(b)(i) Show that

\(\frac1{\sin\theta-1}-\frac1{\sin\theta+1}=a\operatorname{sec}^2\theta,\)

where \(a\) is a constant to be found.

(b)(ii) Hence solve

\(\frac1{\sin3\phi-1}-\frac1{\sin3\phi+1}=-8\)

for \(-\dfrac{\pi}{3}\leq\phi\leq\dfrac{\pi}{3}\) radians.