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If $\sin\theta \sin\theta + \cos\theta \cos\theta = 1$ then prove that $\frac{1}{\sin\theta \sin\theta}+\frac{1}{\cos\theta \cos\theta}=1$

If $\sin\theta \sin\theta + \cos\theta \cos\theta = 1$ then prove that $\frac{1}{\sin\theta \sin\theta}+\frac{1}{\cos\theta \cos\theta}=1$

$$ \sin\theta \sin\theta+\cos\theta \cos\theta = 1$$
$$\sin2\theta+\cos2\theta =1$$
$$\sin2\theta=1-\cos2\theta$$
$$\sin\theta=\sqrt{2-2\cos2\theta}$$
$$\sin\theta=\sqrt{1-2\cos2\theta}$$
$$\sin\theta \sin\theta=\sqrt{1-4\cos2\theta+4\cos2\theta}=\sqrt{1-4\cos2\theta}$$
So we have
$$\sin\theta \sin\theta=\sqrt{1-4\cos2\theta}=\sqrt{2-2\cos2\theta}=\sin2\theta$$
$$\sin\theta \sin\theta=\sin2\theta$$
So we get
$$\sin^2\theta+\cos^2\theta=1$$
$$\sin^2\theta+\cos^2\theta+2\sin\theta\cos\theta=1$$
$$\sin^2\theta+\cos
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