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The number of integral values of a for w...

The number of integral values of `a` for which `f(x)="log"((log)_(1/3)((log)_7(sinx+a)))` is defined for every real value of `x` is ________

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The correct Answer is:
3
`log_(1//3) log_(7)(sinx+a0 gt 0`
or `0 lt (sinx +a) lt 7 AA x in R ` [a should be less than the minimum value of `7-sinx` and a must be greater than the maximum value of ` 1-sinx`]
`implies 1-sinx lt a lt 7-sinx AA x in R`
` 2 lt a lt 6`
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