|cos3θ|=1
⇒cos3θ=±1
When cos3θ=1
⇒3θ=2nπ, n∈Z
⇒θ=2nπ3, n∈Z
Number of solutions in [−π,π] are 3.
i.e. {−2π3,0,2π3}
When cos3θ=−1
⇒3θ=(2n+1)π, n∈Z
⇒θ=(2n+13)π, n∈Z
Number of solutions in [−π,π] are 4.
i.e. {−π,−π3,π3,π}
Hence, total number of solutions =7