Let  θ∈[0,4π] satisies the equation (cosθ+1)(cosθ+2)(cosθ+3)=24, then the sum of all the values of  θ is of the form kπ then K =

# Let  $\theta \in \left[0,4\pi \right]$ satisies the equation $\left(\mathrm{cos}\theta +1\right)\left(\mathrm{cos}\theta +2\right)\left(\mathrm{cos}\theta +3\right)=24$, then the sum of all the values of  $\theta$ is of the form $k\pi$ then K =

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### Solution:

We have $LHS\le 24,RHS=24$

$\therefore LHS=RHS=24$

$⇒\mathrm{cos}\theta =1⇒\theta =0,2\pi ,4\pi$

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