$K^+Lambda(1405)$ photoproduction has been studied at the BGOOD experiment via the all neutral decay, $Lambda(1405)rightarrowSigma^0pi^0$. BGOODs unique experimental setup allows both the cross section and $Lambda(1405)$ invariant mass distribution (line shape) to be measured over a broad $K^+$ polar angle range, extending to extreme forward $K^+$ angles unattainable at previous experiments. The line shape was determined to be in agreement with the previous results of CLAS and ANKE, and appear consistent with two poles derived in $chi$PT based models. %with hints of a double peak structure which may have been observed in the ANKE results At forward $K^+$ angles the relative strength of the peaks appear to change, however more statistics are required for a firm conclusion. Evidence is provided for the role of a triangle singularity driven by the $N^*(2030)$ resonance, which appears to significantly contribute to $K^+Lambda(1405)$ photoproduction. This is observed in both the angular distributions and the integrated cross section which was determined with unprecedented energy resolution.
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