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According to the given condition, if a,b,c are in G.P., we have
ac=b2
Similarly,
tanθsinθ×61=cos2θ
⇒sin2θ=6cos3θ
⇒6cos3θ+cos2θ−1=0
We get cosθ=21 by observation, since its value has to lie between 0 and 1.
Since cosθ=21, the general solution becomes 2nπ±3π
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