Mathematics

The key is recognizing that $1+\cot^2\theta$ is one of the Pythagorean identities—it always equals $\csc^2\theta$. Since you know $\tan\theta$, you can find $\cot\theta$ immediately (it's just the reciprocal), then use that to compute $\csc^2\theta$. This avoids any messy angle-finding and goes straight to what the expression actually means.

The key is recognizing that $1+\cot^2\theta$ is one of the Pythagorean identities—it always equals $\csc^2\theta$. Since you know $\tan\theta$, you can find $\cot\theta$ immediately (it's just the reciprocal), then use that to compute $\csc^2\theta$. This avoids any messy angle-finding and goes straight to what the expression actually means.