Find the values of `theta`, for which `cos3theta + sin3theta + (2sin2theta-3)(sintheta-costheta)` is always positive.

Explanation

Given expression can be written as:
`4cos^(3)theta-3costheta+3sintheta-4sin^(3)theta+(2sin2theta-3)(sintheta-costheta)`
Applying given condtions, we get
`rArr -4(sin^(3)theta-cos^(3)theta) + 3(sintheta-costheta) + (sintheta-costheta) (2sin2theta-3) gt 0`
`rArr -4(sintheta-costheta)(sin^(2)theta + cos^(2)theta + sinthetacostheta)+3(sintheta-costheta) + (sintheta-costheta) (2sin2theta-3) gt 0`
`rArr (sintheta-costheta) {-4 -4sintheta costheta+3+4sintheta-3} gt 0`
`rArr -4(sintheta-costheta) gt 0`
`rArr -4sqrt(2)sin(theta-pi/4) gt 0 rArr sin(theta-pi/4) lt 0 rArr 2npi - pi lt theta-pi/4 lt 2npi, n in I`
`rArr 2npi - (3pi)/(4) lt theta lt 2npi + pi/4 rArr theta in (2npi -(3pi)/(4), 2npi + pi/4), n in I` Ans.