Plus Minus

Geometry Level 4

If we are given that \( (1 + \sin x)(1 + \cos x) = \frac54\), and that \((1-\sin x)(1- \cos x) \) can be expressed as \( \frac ab - \sqrt c \) for positive integers \(a,b,c\) with \(a,b\) coprime, find the value of \(a+b+c\).