if root 3 tan thita = 3 sin thita find the value of sin square - cos square thita

(√3)TanΘ = 3SinΘ

=> (√3)(SinΘ/CosΘ) = 3SinΘ [Using: TanA = SinA/CosA]

=> (SinΘ/CosΘ) / SinΘ = 3 / (√3)

=> (SinΘ/CosΘ) / SinΘ = (√3)² / (√3)

=> 1/CosΘ = √3

=> CosΘ = 1/√3 [Taking reciprocals both sides]

=> (CosΘ)² = (1/√3)² [Squaring both sides]

=> Cos²Θ = 1/3

=> (-2)_*Cos²Θ = (-2)_*(1/3) [Multiplying (-2) both sides]

=> -2Cos²Θ = -2/3

=> 1 - 2Cos²Θ = 1 - 2/3 [Adding 1 both sides]

=> (Sin²Θ+Cos²Θ) - 2Cos²Θ = (3-2)/3

=> Sin²Θ - Cos²Θ = 1/3