The domain of the function f(x)=loge⁡log|sin⁡x|⁡x2−8x+23−3log2⁡|sin⁡x| contains which of the following interval(s)?

f(x) is defined if log∣sinx ∣⁡x2−8x+23−3log2⁡|sin⁡x|>0or log|sin⁡x|⁡x2−8x+238>0This is true if |sin⁡x|≠0,1 and x2−8x+238<1Now, x2−8x+238<1 or x2−8x+15<0or x∈(3,5)−π,3π2Domain =(3,π)∪π,3π2∪3π2,5