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 $$(\sec \theta + \cosec \theta + \cot \theta)$$?

$$\frac{\cos \theta}{1 - \sin \theta} + \frac{\cos \theta}{1 + \sin \theta} = 4$$

$$\frac{cos\theta + sin\theta cos\theta+cos\theta-sin\theta cos\theta}{sin^2\theta - 1}$$ = 4

$$\frac{2cos\theta}{cos^2\theta}$$ = 4

$$cos\theta = \frac{1}{2}$$

$$\theta = 60\degree$$

$$(\sec \theta + \cosec \theta + \cot \theta)$$

= $$(\sec60\degree+ \cosec60\degree + \cot60\degree)$$

= 2 + $$\frac{2}{\sqrt3} + \frac{1}{\sqrt3} = \frac{2\sqrt{3} + 2 + 1}{3} = 2 + \sqrt{3}$$