For real numbers \(a\) and \(b\), where \(a \neq 0\) and \(b \neq 0\), we can find numbers \(\alpha\), \(\beta\), \(\gamma\), \(\delta\) and \(R\) such that \(a\,\cos x + b\,\sin x\) can be written in the following 4 forms:

\(R\,\sin(x + \alpha)\)

\(R\,\sin(x-\beta)\)

\(R\,\cos(x + \gamma)\)

\(R\,\cos(x-\delta)\)

where \(R \gt 0\) and \(0<\alpha, \beta, \gamma, \delta \lt 2\pi\).

What is the value of \(\alpha + \beta + \gamma + \delta\)?

- \(0\)
- \(\pi\)
- \(2\pi\)
- \(4\pi\)