If $\frac{\cos \theta}{1 - \sin \theta} + \frac{\cos \theta}{1 + \sin \theta} = 4, 0^\circ < \theta < 90^\circ$ then what is the value of $(\sec \theta + cosec \theta + \cot \theta)$?

$2 + \sqrt{3}$

\(\frac{cosθ}{1-sinθ}\) + \(\frac{cosθ}{1+sinθ}\) =  4

\(\frac{2cosθ}{1-sin²θ}\) = 4

{ sin²θ + cos²θ = 1 }

\(\frac{2cosθ}{cos²θ}\) = 4

secθ = 2

{ sec60º = 2 }

So, θ = 60º

Now,

secθ + cosecθ + cotθ

= sec60º + cosec60º + cot60º

= 2 + \(\frac{2}{√3}\) + \(\frac{1}{√3}\)

= 2 + √3