Sign Power Tan

Case 1: $\tan\theta = 0$

If $\tan\theta = 0 \Rightarrow \sin\theta = 0$ . Therefore, the original equation will become $0^0$ which is not equal to 1 .

Case 2: $\sin\theta =1$

If $\sin\theta = 1 \Rightarrow \cos\theta = 0$ . Therefore, the original equation will become $1^{\frac{1}{0}}$ which is not equal to 1 .

Case 3: $\sin\theta = -1$ for even exponent.

If $\sin\theta = -1 \Rightarrow \cos\theta = 0$ . Therefore, the original equation will become $(-1)^{\frac{-1}{0}}$ which is not equal to 1 .

Therefore, $\theta = \phi$ . Null set

A lazy solution, but it works so... Got this by elimination: Assumption: One of the options provided with give a correct answer.

case 1: $\theta$ = 0 $\sin {\theta}$ is already $0$ and $0^0$ is undefined thus cannot equal 1.

case 2 : $\theta = \pi$ : Since $\sin{\pi}$ is still zero, the same thing with case 1.

case 3: $\theta = \left\{ \mathbb{R} \right\}$ : Pick any random real number within the constraint. In my case, 3: ${ \sin { 3 } }^{ \tan { 3 } } \cong\ 1.32$

The only remaining option is that $\theta = \phi$